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MARK TO MARKET MANUAL

JUNE/2016

06/08/2016

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TABLE OF CONTENTS

I - INTRODUCTION ........................................................................................... IV

A - MARK TO MARKET PROCESS AT BB DTVM ................. ................................ iv

B - GENERAL PRINCIPLES ................................ ................................................... xi

C - METHODOLOGY OF THE PRACTICES ...................... ................................... xiii

II – APPLICATIONS ................................. .......................................................... 1

A. TERM STRUCTURE OF PRE-FIXED EXCHANGE RATES ........ ....................... 1

B - FEDERAL GOVERNMENT BONDS – PRE-FIXED .............. .............................. 3

1. LTN – Brazilian Treasury Bills .......................................................................... 3

2. NTN – F - BRAZILIAN TREASURY NOTES Series – F ................................... 4

C - GOVERNMENT FEDERAL BONDS – POS-FIXED .............. .............................. 6

3. LFT – Financial Treasury Bills .......................................................................... 6

4. NTN-B – Brazilian Treasury Notes – Series B .................................................. 7

5. NTN-C – Brazilian Treasury Notes – Series C.................................................. 9

6. NTN-D - Brazilian Treasury Notes – Series D ................................................ 10

D - PRIVATE SECURITIES ................................................................................... 13

7. Debentures .................................................................................................... 13

8. Pre-fixed Assets: CDB/RDB and Other Private Securities .............................. 16

9. Pos-fixed Assets Indexed to SELIC Rate or DI: CDB/RDB ............................. 17

10. Term deposit with Special Guarantee from FGC ........................................... 23

10.1. DPGE Pos-Fixed – Indexed to SELIC rate or DI ...................................... 23

10.2. DPGE Pre-fixed ....................................................................................... 27

11. Pos-fixed Assets Indexed to SELIC or DI: CCB rate....................................... 28

12. Pos-fixed Assets Indexed to SELIC or DI: Financial Bill - LF .......................... 31

13. Pos-fixed Assets Indexed to SELIC or DI Rate: NCE ..................................... 38

14. Other Pos-fixed Assets Indexed to SELIC or DI Rate ..................................... 42

15. Mortgage Bills – LH ........................................................................................ 44

16. Private securities indexed to the IPCA – CDB, DPGEs and Financial Bill - LF 46

17. Certificates of Real Estate Receivables - CRI ................................................ 48

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E - ASSETS NEGOTIATED ABROAD ......................... ......................................... 49

18. ADR – American Depositary Receipt ............................................................. 49

19. Fixed Income – Corporate Bonds, Treasury Bonds, Global, CLN, etc. ........... 49

F- VARIABLE INCOME AND FUTURES ....................... ....................................... 50

20. Shares and BDRs – Brazilian Depositary Receipts ........................................ 50

21. Subscription Rights and Receipts of Shares .................................................. 50

22. Rent (or loans) of Shares ............................................................................... 51

23. Futures BM&F/BOVESPA ............................................................................. 51

24. SWAP ............................................................................................................ 52

25. Options .......................................................................................................... 53

25.1. Liquid Options ......................................................................................... 53

25.2. Low Liquidity Options............................................................................... 53

⇒ BLACK & SCHOLES MODEL ..................................................................... 53

25.3. Barrier Options ........................................................................................ 55

⇒ MERTON (1973) E REINER E RUBINSTEIN (1991) MODEL ..................... 55

25.4. Futures Options ....................................................................................... 59

⇒ BLACK MODEL .......................................................................................... 59

25.5. Foreign Currency Options ........................................................................ 62

⇒ GARMAN-KOHLHAGEN MODEL ............................................................... 62

26. Exotic Options ................................................................................................ 64

26.1. QUANTO Adjustment .............................................................................. 64

26.2. Asian Options .......................................................................................... 66

27. Synthetic Operations ...................................................................................... 68

G - FIXED EARNINGS OPERATION – SHARE TERM ......... ..................................... 70

28. Share Term .................................................................................................... 70

H – REPURCHASE AGREEMENTS ......................... ................................................. 71

29. Repurchase Agreements ............................................................................... 71

I – SHARES OF FUNDS ............................................................................................. 72

30. Shares of Investment Funds .......................................................................... 72

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I - INTRODUCTION

A - MARK TO MARKET PROCESS AT BB DTVM

1 Overview of the Process The mark to market process – MtM – the portfolios of investment funds at BB DTVM is performed in compliance with the general principles emanating from CVM Instruction 438, 12/07/2006, of the Securities Commission and their later alterations and recommendations provided for in the Self Regulating Code issued by ANBIMA. 1.1 Considering that the Brazilian Capital Market has low liquidity, the prices

of the assets at which the agents are prepared to buy/sell, are not always found easily.

1.2 In order to become these practices as transparent as possible we shall

detail the hierarchy of the mark to market process formulated by BB DTVM in accordance with the Mark to Market Directives formulated by ANBIMA.

1.3 In the hierarchy of the processes we have:

1.3.1 gathering of the prices; 1.3.2 handling of the gathered prices; 1.3.3 validating of the data/prices handled; 1.3.4 applying of the prices to the portfolios; 1.3.5 validating of the price application to the portfolios; and 1.3.6 dynamic supervision of the methodology.

1.4 Gathering of Prices – the primary sources of which the processes and

methodologies are composed are obtained by downloading files from the following institutions:

- ANBIMA – Federal Government Bonds/Private Securities

(Debentures)

- BM&F/BOVESPA – Derivatives, adjustments to the Futures Market

and ETTJ

- BM&F/BOVESPA – Shares, BDRs and Options

- CETIP – Private Equity

- Various Providers of Market Prices (CMA, BROADCAST,

BLOOMBERG, Others) – International equity

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1.5 Dealing with gathered prices – We describe ahead a detailed

methodology for each asset, where some are treated directly from the source in the form of unitary pricing - UP, others are calculated in accordance with their rates or quota, in consideration of the standard methodologies used by the market for each asset, albeit:

1.5.1 Capitalization period – daily, monthly, semester or annual; 1.5.2 Capitalization – linear or exponential; 1.5.3 Number of days counted – 252 working days of the year, days

360, 30/360 consecutive days; 1.5.4 of payments - month, semester, annual, etc.

1.6 Validating the handled prices - final edition of the handled prices is made

by way of a comparative analysis between the daily yield, in search of the adherence of the yield used by the market.

1.7 Applying the prices to the portfolios – Prices calculated in accordance to

rates are made available to the team that is responsible for processing the portfolios on the Board Solutions Wholesale – DISAT, by way of their own software, whereas prices used for portfolios are gathered by the processing team directly from the primary source.

1.8 Validating the application of prices to portfolios – The Processing

Division from DISAT makes an analysis of price deviation, checking its coherence with the market of the referred Asset. The external auditors run periodic tests to validate the pricing and the internal auditors run periodic evaluates the process of mark to market with a focus on risk.

1.9 Dynamic supervision of the methodology – Follow-up of the processes in

the order shown is performed by the division that is responsible for the mark to market process.

2 Methodological Aspects

2.1 The team responsible for processing funds and portfolios gather, on a daily basis, the Ups, rates or quotas, in accordance with each case, by way of their own applications and closure of the markets.

2.2 For funds that work with opening quotas, the quota is calculated by the

Methodologies Team from DISAT based on the earnings projection observed for each asset that makes up the portfolio of the fund on d-zero updated for d+1, date of the quota.

2.2.1 The opening quota shall be updated in accordance with the

following:

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a - estimated appreciation of the assets in the portfolio, observed in the markets on D0;

b – Weighing the appreciation of the assets, with respect to the percentage of Net Equity.

( ) 01 −×+= dab cic

Where:

• Cab = opening quota D+1 • i = index for updating quota • Cd-0 = opening quota on D0

2.2.2 Alternatively, in case of inoperable system, communication

failure, the opening quota may be updated by the DI effective on the day, in accordance with the following:

0

252

1

1100 −×

+= dab ci

c

Where:

• Cab = opening quota D+1 • i = rate of DI of the day, seen on D0, • Cd-0 = opening quota D0;

3 Organizational Structures involved in the process

3.1 The organizational structure at BB DTVM includes a directorship made up of the Chairman, Two Senior Directors, and Seven Senior Managers, who participate in the forums and committees detailed below in item 3.5.

3.2 The MTM process is conducted by the Board Solutions Wholesale –

DISAT, Banco do Brasil S.A., through the Funds Controller Division, composed of a division manager, two team managers, who are responsible for the balance sheets of the funds and a team of analysts, who are responsible for assessing, testing and proposing methodologies for mark to market and pricing of financial assets.

3.3 The Funds Controller Division is linked to the Fiduciary Services

Management - DISAT, therefore segregated from the Senior Managers of Fund Management, owned by BBDTVM.

3.4 The methodologies are developed in accordance with the

characteristics of each asset or group of assets and the models are

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then forwarded to the BBDTVM directors through Notes awaiting approval

3.5 The Statute of the BB DTVM foresees that the distributor should adopt

a group decision at all levels. The existing forums and committees are listed below:

3.5.1 Forums

� Strategic Forum; � Amplified Forum; � Analysis of Economic Situation; � Stock Market Analysis.

3.5.2 Committees

� Asset Management Committee; � Allocation Committee; � Product Committee; � Credit Committee and the Funds Governance ; � Risk Committee; � Asset Pricing Committee; � Information Technology Committee; � Performance Evaluation Committee; � Management Committee; � Committee Structured Funds; � Communication and Marketing Committee.

3.5.3 Asset Management Subcommittees.

� Subcommittee on Management of Fixed Income; � Subcommittee on Management of Shares; � Subcommittee Management of Multi-Market and Offshore; � Allocation Subcommittee.

3.5.4 The Committee Regiment for Asset Pricing are provided below,

taking into consideration what it truly has a jurisdiction to discuss on to Mark to Market subjects

Article 1 – MEMBERS – The Asset Pricing Committee shall be made up of:

a) Full Members: I. Executive Manager of Management Funds;

II. Executive Product Manager; III. Division Manager of Fiduciary Services; IV. Division Manager of Management Structured Funds.

b) Alternate Members: appointed by the holders.

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c) Members Invited – Permanent participation, without voting rights:

I. Division Manager of Market Operations;

II. Compliance Manager; III. Division Manager of Credit Analysis; IV. Division Manager for Modeling Market Risk and

Liquidity Funds; V. Division Manager of Fund Controllers - DISAT; and

VI. Business Consultant from Division Fund Controllers - DISAT.

Paragraph 1 – The full members may only be substituted by the respective alternate members in case of vacation, sabbatical, paid leave, attendance allowance, time off, training or business trips. Paragraph 2 – The members invited in his absence will be represented by officials of the respective Divisions indicated by them. Article 2 – RESPONSIBILITIES:

I. To analyze and propose to the Directors inclusions/alterations/updates of asset pricing methodologies to the fund portfolios; II. Accompany and analyze the market conditions, and propose adjustments/modifications to the asset prices, in consequence of moments of crisis on the market or low liquidity; III. Assess and validate the information on prices gathered and supplied by the Market Operations Division; IV. Assess and validate the ratings information used in asset pricing, supplied by the Credit Analysis Division; V. Validate the baseline prices used for Interpolation/extrapolation of rates, for asset pricing; VI. Assess and validate price ranges to be used in asset pricing; VII. Assess and improve the cutting points in the samples used for the price ranges;

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VIII. Define materials that may be submitted to the members of the Committee for deliberation, using mechanisms for consultations/response by e-mail; IX. Other subjects pertinent to asset pricing. Sole paragraph – The responsibility of the members of the Committee for omission in the execution of their duties is solidarity, and yet shall excuse the member who may duly given reason for the diversions in the minutes of the Committee Meeting.

Article 3 - THE MEETINGS – The Committee shall hold ordinary meetings on the last Thursday of each month, or extraordinary meetings whenever determined by its Coordinator. Article 4 - THE QUORUM – The minimum quorum for the installation of the Committee is 03 (three) members, the presence of the Coordinator or alternate member. Article 5 - CRITERIA FOR DELIBERATION – decisions of Committee shall be taken unanimously or by a simple majority vote of its members entitled to vote.

Article 6 - THE COORDINATION – coordination shall be exercised by the Executive Manager of Management Funds. In his absence, the coordination shall be exercised by one of the other permanent members of the Committee, indicated by him. Article 7 - GUESTS – In addition to the permanent members, representatives from other areas may be invited to participate in meetings without the right to vote, to provide clarifications relevant to the matters at hand. Article 8 – SECRECY – The materials are confidential by nature and those that are discussed by the committee shall be kept in secret by the members present at the meeting, as well as those to whom the aforesaid has come to their knowledge. Article 9 - THE MINUTES – The minutes shall be written in a clear and concise manner. The documents used for background information for the decisions shall be attached and kept for a minimum of 10 (ten) years. Article 10 – SECRETARIAT – The Committee shall establish a Secretariat, whose activities are carried out by one of its members, who will be responsible:

I. Call and ask staff to stakeholders;

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II. Prepare and distribute meeting agendas and copies of documents, with at least two days prior to the date of realization, except where expressly authorized by the Coordinator; and

III. Prepare minutes of meetings and collect the signatures of its members.

Sole Paragraph – In the Governance and Planning Division to keep fit in their custody the documents concerning the activities of the Committee.

Article 11 - GENERAL PROVISIONS – The senior directors shall remove any existing doubts related to this regiment, as well as provide modifications that may be judged necessary and decide on pending cases..

3.6 Since approved, the methodologies for calculation will be sent to the

information technology division, to develop systems/applications, if necessary, for the purposes of making the processes operational thus requiring less manual interference.

3.7 Once having been placed in production, the methodology is applied

uniformly to all assets owned by BB DTVM, whose funds contemplated in the Contract for Qualified Services to the Capital Markets and controllership services whose assets are in charge of Funds Controller Division - DISAT, including exclusive funds. Except for the referred procedure: funds under custody of other assets or financial institutions, funds whose shareholders have decided to classify their assets in accordance with item 1.2.2.3 from CVM Instruction 438, 12/07/2008, – Securities kept up to maturity.

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B - GENERAL PRINCIPLES

These principles are considered to be guidelines for establishing the policies of MTM and are used as directives for the processes and practice of Mark to Market, and should be applied in a coherent manner, that is, the way in which one is applied shall not interfere in the application of another, in order to perform the MARK TO MARKET – MTM. 1. Best practices

The process and methodology of MTM must follow the best practices of the market.

2. Scope

Taking the view that the principal purpose of Mark to Market is to avoid the transfer of wealth between various shareholders of an investment fund, these directives cover all non-exclusive and non-restrictive funds, that is, those in which the aforesaid transfer of wealth needed to be avoided. Under these measures, for the purposes of these directives, and exclusive funds is that which is determined exclusively to one investor and restricted fund is that which is destined to a group of determined investors, who have amongst themselves family ties, partnerships or belong to the same economic group, or in writing determined this condition. In case an investment fund lose its characteristic of exclusive or restrictive fund, then the general rules of other funds shall be immediately applied to it.

3. Commitment

The administrator of the fund should be committed to guaranteeing that the prices reflect the market, and whenever this should prove to be impossible, take all necessary measures to estimate what would be the market prices of assets for which these would be effectively negotiated.

4. Equality

The preponderant criteria used in the process of choosing the methodology, data source and/or any decision for MTM must be treated equally among the shareholders.

5. Frequency

The MTM should have as a minimum frequency the periodic calculation of quotas.

6. Formality

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The administrator of the fund should have a formal process for handling MTM. For this purpose, the methodology should be defined in the MTM manual and the institution should have a department or person responsible for the execution, quality of both the process and methodology, as well as safekeeping of documentation that contains the justification for the decisions taken.

7. Objectivity

The information on prices and/or factors to be used in the MTM process should be obtained preferably from external independent sources.

8. Consistency

If the administrator is responsible for the pricing of all his funds, a same asset cannot have a different price in any of the funds. In case of hiring the service from qualified provider:

8.1. In analogous form, if one or more of the funds of the same

administrator, the pricing comes under the responsibility of an outsourced service provider, under these funds, a same asset may not have a different price when the same MTM manual is used; and

8.2. The outsourced service provider may not adopt for the same assets,

even when in different funds and from different administrators, different prices when using the same MTM manual, outsourced service provider, neither adopt for the same assets, even in different funds and with different administrators, different pricing, when using the same MTM Manual, to determine consistency in the performance of his duty.

9. Transparency

The methodologies of mark to market must be both published and available.

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C - METHODOLOGY OF THE PRACTICES

1. Should be used as a primary source for prices:

• Federal Government Bonds: ANBIMA

• Shares, BDRs, share options, share term: BM&F/BOVESPA

• Illiquid options: mathematical models, statistics, Black & Scholes, etc.

• Futures contracts, swaps, commodities (agricultural): BM&F/BOVESPA

• Private securities: ANBIMA (Debentures), mathematical models and statistics, in the absence of a consistent secondary market.

• International securities: CMA, BROADCAST and BLOOMBERG.

2. Contingency or alternative form of pricing

2.1. Federal Government Bonds

For the purposes of a contingency, or even as an alternative form of pricing, the unit pricing of government bonds are calculated daily and based on the rentability observed on d-1 and updated for d+0, as explained below:

2.1.1. Pos-fixed Assets -is used as an alternative for pricing fixed earning assets, Pos-fixed, when the primary source is not available, in order of preference:

a - Updating of the Ups on D+0, based on the earning ability observed in the primary source between D-2 and D-1.

b - when it is impossible to check the earning ability at the primary source, between D-2 and D-1, use the respective up dating rate on day 1 of the index, or, TMS, CDI, etc, as shown in the sample below:

252

1

1100

+= ifat

Where:

• fat = update factor • i = rate expressed in one year by the asset index

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2.1.2. Pre-fixed Assets - have the following alternatives for pricing in order of use, if the primary source is not be available:

a - are priced by taking the term structure rate described in this

manual, adding the premium seen at the last auction held by the Brazil Central Bank.

b - secondarily, if it is not be possible to use the ETTJ the prices are adjusted on D+0 based on the ETTJ for the previous day ( d-1 ).

2.1.3. Pos-fixed assets indexed to the price index -have the following

alternatives for pricing in order of use, should the primary source not be available:

a - update of the Ups on D+0, based on the earnings observed

that the primary source between D-2 and D-1.

b - Secondarily, should it not be possible to check the earnings at the primary source between D-2 and D-1, the Internal Rate of Return published by the primary source on D-1is use the as a parameter.

2.2. Assets with primary source indicators from the BM&F/BOVESPA

For contingency purposes, or even as an alternative form of pricing for assets that have as their primary source indicators from the BM&F/BOVESPA, information from D-1 shall be repeated in D-0 2.2.1. Whenever there is a stop in trading (Circuit Breaker), information

supplied by the BM&F/Bovespa is used.

3. Shares, BDRs, options on liquid shares and Share Term

The BM&F/BOVESPA itself reveals the quotas traded on the stock market. In case of illiquid options mathematical and statistics models are used for the attribution of price, among we list: Black & Scholes or Black, as the case may be.

4. Futures, Swaps and Commodities Contracts

The derivative operations are carried out in specialized clearing, and the Stock and Futures Market /BOVESPA are the greater daily trading.

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5. Assets in Default

All assets are marked for the market, for which their respective criteria are observed. As a consequence the value of the asset corresponds to that which would be obtained should it be sold in the same market. Once the assets accompany the movements of the market, their prices shall reflect the perception of risk of the economic agents. In the case of observing the non-payment of installments, amortization or principal, then the following stages shall prevail:

5.1. The processes relative to the recuperation of credit are made directly

by the senior director, with help from the credit analysis division and the respective administrators.

5.2. Once default of payment installments, amortization or principal is

detected, extrajudicial negotiations begins between the representatives of the BB DTVM and the respective debtors.

5.3. In parallel with these negotiations with the Senior Directors shall

determine provisions for the operation value. 5.4. Should the extrajudicial negotiations prove to be unsuccessful then

judicial proceedings will be brought against the debtor(s), to recuperate part or the entire investment amount.

5.5. In case of recuperation the provision shall be reverted, otherwise, the

operation shall be accounted as a loss and removed from the fund.

6. Occurrences of systemic and market risk

Administering financial assets, like all other financial economic activities, are subject to unexpected events that may cause oscillations in the value of the assets impacting significantly on the equity of the funds. Certain occurrences, even though they may in some way be known, that is, classified by the doctrine, are in most cases unpredictable. In the case of moratorium between emerging countries, external crisis in the energy sector – oil, exchange rate crisis in strong currencies – such as the Dollar and the Euro, American economic recession, amongst others. These factors may –– or not – cause strong impacts on the Brazilian economy and consequently on the financial assets.

Each crisis has its own characteristic and reflexes making it impossible to plan actions and procedures, and as the same can only be determined case-by-case. The decisions, depending on the subject, are taken at the following Forums:

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6.1. Strategic Forum 6.2. Increased Forum

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II – APPLICATIONS

A. TERM STRUCTURE OF PRE-FIXED EXCHANGE RATES

1. The term structure of exchange rates was developed to create

parameters for pre-fixed pricing of fixed earning assets.

2. The referred to structure consists of creating an interest curve, based on trading on the Interest Rate Future Markets at the BM&F/BOVESPA.

3. In the absence of intermediary points on the curve is used the interpolation exponential method; in the case of extrapolation one repeats the last forward in the construction of the curve.

4. The contracts of the DI are traded by an express yearly percentage rate and its liquidity occurs at the final value of R$100.000,00. The UP – unit price, seen daily, is obtained using the interest rates of the contract, discounting the same from the 100.000 amount, as shown below:

Where: • PU = unit price;

• 100.000 = vlr. at maturity of contract;

• i = interest rates;

• bd = business days until the maturity of the contract.

5. The interest rates of a contract, from the UP, can be calculated in accordance with the following formula :

1001000.100 252

xPU

i bd

−

=

( )

+=

2521100

000.100bd

iPU

2

Where:

• i = Interest rates per year (base 252 du);

• PU = Unit price traded on the market;

• 100.000 = Base value of contract1;

• bd = business days.

6. Having seen the necessity to obtain rates for periods where there is no trading, we use the mathematical concept available known as the interpolation technique.

7. We adopt the exponential interpolation criteria using the following formula:

=

2

1

2

1

1

00,000.100

00,000.100

bd

bd

UP

UP

UP

PUy

Where:

• PUY = UP to be obtained by way of interpolation;

• pu 1 = UP with liquidity, before the vertex without liquidity;

• pu 2 = vertex with posterior liquidity UP1;

• bd1 = number of business days before the maturity of the UPy and the PU1;

• bd2 = number of business days between the maturity of the UP2 and the PU1

8. Having obtained the PU, apply the formula in item 5, to extract the respective interest rates.

9. Source:

� primary: future interest market at the BM&F/BOVESPA.

� Secondary: Term Structure for Interest Rates released in the ANBIMA table.

1 Presently the value of the Future Contracts for DI is R$100,000.00, in accordance with clause 2, defined by the BM&F.

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B - FEDERAL GOVERNMENT BONDS – PRE-FIXED

1. LTN – Brazilian Treasury Bills 1.1. Characteristics:

1.1.1. term: defined by the Brazilian Treasury, when issuing the bonds;

1.1.2. mode: nominative

1.1.3. nominal value: multiples of R$1.000,00 (thousand Reais);

1.1.4. earnings: defined by the discount on the nominal value

1.1.5. redemption: for the nominal value, on date of maturity 1.2. The Brazilian Treasury Bills are not accounted for on a daily basis with unit

prices – PU – they are calculated by of discounted cash flow, using as a discount factor the interest rates priced in the market by the maturity of the bond

1.3. Methodology

The Brazilian Treasury Bills - LTN are priced in accordance with the following formula:

( ) 2521100

.BD

i

RVPUMtM

+=

Where:

• PUMtM = UP of the market

• V.R. = Value at maturity – VR = 1.000,00

• i = pre-market interest rates for maturity

• BD = business days accumulated between the present date until the maturity of the asset

1.4. Source

� Primary: ANBIMA table. � Secondary: Structural Terms of Interest Rates, detailed above, with

respective spread.

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2. NTN – F - BRAZILIAN TREASURY NOTES Series – F 2.1. Characteristics:

2.1.1. term: defined by the Brazilian Treasury, when bond is issued;

2.1.2. interest rates: defined by the Brazilian Treasury, when issuing, in the yearly percentages, calculated at nominal value;

2.1.3. mode: nominative;

2.1.4. nominal value: multiples of R$ 1.000,00 (thousand Reais);

2.1.5. yield: defined by the setting concession on the nominal value;

2.1.6. Interest payments: every semester, with adjustment of the term during the first period of flow, should it be the case. The first taxes to be paid shall be at full tax rate for the first six months, independent of the date the bond was issued;

2.1.7. redemption: at the nominal value, on the date of its maturity. 2.2. The Brazilian Treasury Notes – series F - are accounted daily with the unit

price – PU – calculated by discounted of cash flow, used as a factor for internal tax discount the internal rate of return for the maturity of the bond.

2.3. Methodology

The calculation model of the market for this asset brings the cash flow to present value, taking into consideration the given internal rate of return - TIR, as we can see, considering the interest for six months at 10% per year:

( )

( ) ( )∑= +

++

−+=

n

iBDnBD

TIRTIRCOT

i1 252252

21

1100

1

1100

1110010

VNCOTVP ×=

Where: • BDi – number of business days between the present date and the

date of payment of the ith interest;

• BDn – number of business days between the present date and the redemption;

• TIR –interest rate of return;

• COT – quota, percentage of the nominal value;

• VP – present value;

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• VN = 1.000,00;

2.4. Source: � Primary: the PUs daily released in Table ANBIMA, calculated

according to the indicative rate. � Secondary: structure term of interest rates, adjusted in accordance

with the spreads.

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C - GOVERNMENT FEDERAL BONDS – POS-FIXED

3. LFT – Financial Treasury Bills 3.1. Characteristics:

3.1.1. term: defined by the Brazilian Treasury, when the bonds are issued;


3.1.3. nominal value on database: multiples of R$ 1.000,00 (one thousand Reais);

3.1.4. yield: average adjusted rate of daily financing provided by the Special System for Settlement And Custody - SELIC for federal government bonds, released by the Brazilian central bank, calculated at its nominal value;

3.1.5. redemption: by the nominal value, plus the respective yield, from the base date of the bond.

3.2. The Financial Treasury Bills are accounted daily with unit price – PU –

calculated using discounted cash flows, using as discount factor the premium/discount priced by the market for the maturity of the bond.

3.3. Methodology

The LFT are priced in accordance with the following formula:

( ) 2521100

238_BD

i

PUPUMtM

+=

Where:

• PUMtM = unit price marked by the market. • PU_238 = UP there released by BACEN by way of the nominated table

Resolution 238. This PU is defined as the PU at issue, corrected by the average accumulated SELIC rate.

• i = annual premium rate or discount applied to the maturity of the asset. • BD = accumulated business days between the present date until the

maturity of the asset. 3.4. Source

� Primary: the Pus daily released in the Table ANBIMA, calculated according to the indicated rate.

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� Secondary: the variations between the PUs of D-2 and D-1.

4. NTN-B – Brazilian Treasury Notes – Series B 4.1. Characteristics:


4.1.2. interest rates: defined by the Federal Treasury, on issue, in yearly percentages, calculated on the updated nominal value.


4.1.4. nominal value at base date: multiples of R$ 1.000,00 (one thousand Reais);

4.1.5. update of nominal value: by the variation in the Ample Consumer Price Index - IPCA for the previous month, released by the Brazilian Institute for Geography Statistics Foundation (Fundação Instituto Brasileiro de Geografia e Estatística) - IBGE, from the base date of bond;

4.1.6. Interest payments: every semester, with adjustment term on the first period of flow, whenever applicable. The first coupon of interest to be paid shall include the full rate defined for the six months period, independently of the date the bond was issued;

4.1.7. Redemption of the principal: in lump sum on date of maturity.

4.2. The Brazilian Treasury Notes – series B - are accounted daily with the unit price – PU – calculated using discounted cash flow, using the internal rate of return– TIR priced by the market for the maturity of the bond.

4.3. Methodology

The calculation model of the market of this asset bring the cash flow to the present value, taking into consideration a given internal tax rate on return - TIR, as we see:

( )( ) ( )∑

= ++

+

−+=

n

iBDnBD

TIRTIR

iCOT

i1 252252

21

1100

1

1100

11100

Where:

8

• BDi – number of business days between the present date and the date of payment ith of interest;

• BDn – number of business days between the present and redemption dates;

• TIR – internal rate of return;

• COT – quota, percentage of corrected nominal value;

• VNA – nominal value updated by the last 15th day of the month –parity;

• BDn – business days between the present date and the last 15th of the month;

• BDt – business days between the last 15th and the next 15 of the month, in relation to the present date;

• VNA corrected – nominal value updated and corrected for the present date;


• i – interest rates of the asset;

• FatIPCA - IPCA variation factor between the base date and the last 15th previous to the present date;

• IPCAforecast – expected IPCA for the period.

)(*00,000.1$ FatIPCARVNA =

t

nBD

BD

stIPCAforecaVNAedVNAcorrect )1(* +=

VP = quota * VNACorrected

4.4. Source

� Primary: the PUs released daily in the Table ANBIMA, calculated on the indicated rates.

� IPCA forecast: it is used the average checked by the commission for

accompanying macroeconomics from ANBIMA and may be used, alternatively, the ample consumer price index – IPC-A, defined by the Macro-Economic Distributor Division.

� Secondary: are used the rates released by ANBIMA on D-1.

9

5. NTN-C – Brazilian Treasury Notes – Series C 5.1. Characteristics:


5.1.2. interest rates: defined by the Brazilian Treasury, on issue, in yearly percentages, calculated on the updated nominal value;


5.1.4. nominal value on base date: multiples of R$ 1.000,00 (one thousand Reais);

5.1.5. update of nominal value: by the variation in the Market Price Index - IGP-M for the previous month, released by the Fundação Getúlio Vargas, from the base date of the bond;

5.1.6. Payment of interest: every semester, with term adjustment in the first period of flow, whenever applicable. The first interest coupon to be paid contains full tax rate for the six months, independently of the date the bond was issued;

5.1.7. Redemption of principal: in lump sum, on the date of its maturity.

5.2. The Brazilian Treasury Notes– series C - are accounted daily by unit price – PU –calculated by discounted cash flow, using the internal rate of return – TIR priced by the market for the maturity of the bond.

5.3. Methodology

The calculation model of the market for this asset bring the cash flow at the present value, taking into consideration the given internal rate of return - TIR , as we see:

( )( ) ( )∑

= ++

+

−+=

n

iBDnBD

TIRTIR

iCOT

i1 252252

21

1100

1

1100

11100

Where:

• BDi – number of business days between the present date and the date of payment of the ith interest;

• BDn – number of business days between the present and redemption date;

• TIR – internal rate of return; • COT – quota, percentage of adjusted nominal value; • VNA – nominal value updated to the last day 1 – parity;

10

• BDn – business days between the present date up to the last day 1; • BDt – business days between the last day 1 and the next day 1, in

relation to the present date; • VNA cor – nominal value updated to the present date; • VP – present value; • i – interest rates of the asset; • FatIGP-M - variation factor in the IGP-M between the base date and the

last day 1 before the present date; • IGP-Mforecast – expected IGP-M for the period.

)(*00,000.1$ MFatIGPRVNA −=

) t

nBD

BD

MforecastIGPVNAVNAcor −+= 1(*

VNAcorVP cot*= 5.4. Source

� Primary: the PUs released daily in the Table ANBIMA, calculated on the indicated rates.

� IGP-M: it is used the average checked by the Commission for

Accompanying Macroeconomics from ANBIMA, for the month (except for the following day after the release of the final IGP-M, whenever the index itself is used for the current month, published by the FGV), alternatively, the IGP-M defined by the Macro-Economic Distributing Division may be used.

� Secondary: the rates published by ANBIMA in D-1.

6. NTN-D - Brazilian Treasury Notes – Series D 6.1. Characteristics:


6.1.2. interest rates: defined by the Brazilian Treasury, at issue, as a percentage per year, calculated on the nominal updated amount;


6.1.4. nominal value at the base date: multiples of R$ 1.000,00 (thousands of Reais);

6.1.5. update of nominal value: by the variation of the quotation for sale of the US dollar on the free-rates exchange market, published by

11

the Brazilian Central Bank, considering the average rate of the day immediately prior to the base date or the date of maturity of the security;

6.1.6. payment of interest: every six months, with adjustments in the term in the first period of influence, whenever applicable. The first interest coupon to be paid shall consider the full rate defined for six months, independently of the date of issue of the security;

6.1.7. redemption of principal: in one lump sum on the maturity date.

6.2. The Brazilian Treasury Notes – series D – are accounted daily with unit prices – PU – calculated by discounted cash flow using the internal rate of return - TIR priced by the market for maturity of the title.

6.3. Methodology

The model for calculation of the market for this asset translated into bringing cash flows to the present value taking into account a given internal rate of return - TIR, as we can see:

( )( ) ( )∑

= ++

+

−+=

n

iBDnBD

TIRTIR

iCOT

i1 252252

21

1100

1

1100

11100

Where:

• BDi – number of business days between present date and date of payment of the i-th interest;

• BDn – number of business days between present date and redemption;

• TIR – internal rate of return;

• COT – quota, percentage of corrected nominal value;


• i – interest rates for asset

−×=)(

11000

eptax

ptaxDVNA

Where:

• VNA – Updated nominal value;

• PtaxD-1 – dollar quotation of D-1, informed by BACEN,

12

PTAX transaction, sales point, commercial dollar;

• Ptax(e) – dollar quotation for working Day immediately before the issue date of the asset, informed by the BACEN (Central Bank), PTAX transaction, sales point, commercial dollar.

VNACOTVP ×=

Where:


• COT – quotation, percentage of corrected nominal value;

• VNA – updated nominal value.

6.4. Source

� Primary: the PUs released daily in the ANBIMA table, calculated on

the indicated rates. � PTAX – published daily by SISBACEN. � Secondary: the Internal Return Rates are obtained in the futures

market of Exchange Coupons of BM&F.

13

D - PRIVATE SECURITIES

7. Debentures 7.1. As marking to market of Primary Source – MtM of the Debentures, used

to price daily unit of calculation purposes quotes provided by Market Table Secondary ANBIMA Debentures. In the case of the Debenture not included in that Table, we use the model of the Secondary Source for marking to market. For cases in which the ANBIMA fails to inform the price of any asset is used the last quotation published, up to a maximum period of 15 working days. Thereafter, the debenture also happens to be priced by the criteria of the model Secondary Source.

7.2. As a Secondary Source of mark to market – MtM of the Debentures,

used in the model Credit Curves ANBIMA, extracted from the debentures Percentage DI, DI + Spread and IPCA + Spread priced daily by this association, since they reflect zero-spread structures code on the sovereign curve for different risk levels. The tool sets a benchmark for the pricing of private credit assets.

7.3. The Debentures are classified by credit risk. However, ANBIMA, Credit

Curves are only calculated for the AAA, AA and A risks (disregard the signal variations within the same scale, that is, there is no distinction between classifications: neutral, plus and minus).

7.4. For the calculation of the mark to market credit spreads, we use the risks

provided by ANBIMA (AAA, AA and A), the respective curves. For other levels of risk, until they start to be available, will be used the extrapolation rule (from the Risk A from ANBIMA) in the following table:

7.5. Considering all adjustments applied by ANBIMA on the model of credit curve, such as risk spreads are only average, adjustments in the level of slope and curvature of curves, lack of standardization in the nomenclature of notes issued by rating agencies, elimination debentures with clauses of early repurchase, insertion of synthetic securities short

Rating BB DTVM Rule

BBB Rating A + 150 base points

BB Rating A + 360 base points

B Rating A + 660 base points

CCC Rating A + 1.080 base points

CC Rating A + 1.760 base points

C Rating A + 3.010 base points

RD Rating A + 7.080 base points

14

term, heterogeneity of issuers and also, comparative studies of the model rates with rates of debentures of de daily pricing of that Association, we made a shift of credit curves, as shown below:

Table 1 – Table of equivalence used in the MtM of the Debentures

TABLE OF EQUIVALENCE OF CLASSIFICATION RISK OF DEBE NTURES

Credit Curve ANBIMA AAA** AAA AA A BBB* B* B* CCC* CC* C*

Risk Debentures in the Model AAA AA A BBB BB B CCC CC C RD

*New ratings created by extrapolation rule. **Credit synthetic curve created from the difference between AAA and AA

Credit risk curve ANBIMA less the AAA risk.

7.6. Within each risk group in their respective maturity dates, daily calculate the average of all Credit Curve rates ANBIMA the last 15 working day.

7.6.1. The Pricing Committee of Assets of BB DTVM can change the

number of working days catch ANBIMA Credit curve to compose the average.

7.7. Known average calculate the standard deviation of credit curves ANBIMA

the last three (3) months. The Upper and Lower Limit correspond to +/- 1 (one) Standard deviation, as well as an indicative range in spread (Fees Acceptance Tunnel). These intervals are transformed into DI Percentage (rate “DI” from the DI Future Interest Rate Curve BM&FBovespa).

7.7.1. The Pricing Committee of Assets of BB DTVM at any time can

apply a modifier (Mod) on the average Credit Curve ANBIMA, aiming to adjust rates in extreme market situations, as well as, you can also change the standard deviation.

7.7.2. The Pricing Committee of Assets of BB DTVM can differentiate he

individual rating of any issuer. 7.8. Daily Debentures are separated by maturity and risk contemplating the

timing and risks of Credit Curve ANBIMA. 7.9. All Debentures whose rates are within the Acceptance Tunnel are

marked to market by the hiring rate or the last marking to market rate used. The Debentures that their rates are out of Acceptance Tunnel, are marked to market with the closest limit Acceptance Tunnel.

7.10. Determination of Tunnel Acceptance of Exchange Rate and consequent

Mark to Market with modifier (Mod):

iMtM Mod = [( µi + / - Mod ) + / - σ ]

Where:

15

• iMtM Mod– mark to market reference rate with the modifier

(Mod) • µi – average frequency rate

• σ – standard deviation of the frequency rates

• Modifier (Mod) – determined by the Asset Pricing Committee.

7.11. The unit price curve (PU PAR) is the value of the Debenture t a given

date, expressed in national currency. Their calculation is performed by updating the title of the issue price as standardization of ANBIMA calculation methodology.

7.12. For Linked Debentures to the IPCA, plus the credit curve ANBIMA, the

mark to market model uses the Term structure of Interest Rates Estimated – ETTJ ANBIMA where sovereign zero-coupon yield curves are extracted from the rates of government securities and fixed rate pegged to the IPCA, plus the implicit inflation cornering.

7.12.1. In contingency situation will be used ETTJ IPCA Estimated

structure of ANBIMA T-1. 7.13. The MtM rates of each Debenture, from the Credit ANBIMA curves (plus

ETTJ the rete estimated IPCA ANBIMA for the Debentures in IPCA), are transformed into Quotation (% of PU PAR) by the Bloomberg system.

7.13.1. For Debentures that the Bloomberg system does not support the

calculation, the MtM Quotation shall be determined by the Pricing Committee of BB DTVM through the Asset Analysis Crusade information with other Debentures, considering the time, risk and similar indexes.

7.13.2. For Debentures that may not behave the Bloomberg system and

the calculation does not apply to use of Analysis Crusade (debentures nonstandard or containing uncertainties on financial events) may take the form of calculation of MtM Quotation defined Pricing Committee Assets BB DTVM.

7.14. The final PU will be given by:

Where:

• PUMtM = UP marked to market;

• C = Quotation (% of PU PAR);

• PUPAR = Unit Price Curve

PUPARCPUMtM *=

16

7.15. For new acquisitions, its starting price record in the system will be the PU or purchase quotation. The effects of marking to market only occur on T+1.

7.16. Unable to apply the MtM model of the Debentures will be used in emergency character / contingency, the Quotations defined in T-1.

7.17. Source

� Primary: Quotations published in the ANBIMA Debentures table.

Absence of publishing of quotations by ANBIMA shall result in the use of the latest quotation for a maximum period of 15 days, and after this period the model described in item 7.2 shall be adopted.

� Secondary: If there is no publishing of the quote in ANBIMA table,

the model described in item 7.2 onwards shall be used.

8. Pre-fixed Assets: CDB/RDB and Other Private Securities

8.1. The pre-fixed assets are traded taking as a base an additional spread

over the interest rates negotiated at the BM&F/BOVESPA, as a premium and/or credit risk spread.

8.2. The credit risk spread and/or premium is defined by the difference when

buying, between the acquisition rate and the equivalent rate at 100 % of the interest curve seen at BM&F/BOVESPA.

8.3. Thus, starting from the principle that the credit risk spread is defined in

the act of acquisition the asset, its present value shall be calculated by the following equation:

( )[ ]( )2521100

n

Si

VRVP

++=

Where: • VP = present value; • VR = redemption value; • i = interest rate; • n = business days until maturity; • S = spread.

8.4. If some private security presents a credit spread lower than the credit

spread for Brazilian treasury bonds – LTN, of the same duration, for the effects of pricing, the greater spread shall prevail.

17

8.5. The CDB classified at the CETIP with condition of anticipated redemption, subject to the present market conditions prevailing at the time of its request was made, may be accounted on its acquisition curve.

8.6. The issuers is of the CDBs are classified in accordance with their credit

risk, by the team responsible for analysis of companies and financial institutions. The reassessment is performed periodically.

8.7. If the Credit Analysis Division note an alteration of the credit risk of an

issuer, in that his rating had been changed, the Controller Division, through its methodology team, shall change the issuer to the new category, with the premium level to this new category. The administrator shall employ his best efforts in order to identify the alterations to the credit risk of the assets, imputing to the prices such alterations.

8.8. Reclassification of the issuer to another category of risk shall lead to an

alteration to his spread.

9. Pos-fixed Assets Indexed to SELIC Rate or DI: CDB/RDB

9.1. Due to the absence of a secondary asset market that could provide

volume, rate and issuing, a mark to market model was developed for the CDBs which use as a base and parameters trading over the last 15 days in the investment funds of the BB Resources Management DTVM S.A., auctions and/or consulting made on the market and primary registered issues on the CETIP.

9.2. Initially the nominal corrected value was calculated, through the following

steps, for daily updates of the unitary prices of a CDB/RDB purchased at a percentage of the CDI/SELIC rate:

Step 1: check the correction factor or accumulated factor

( )( )∏

=

+

∆

−+=n

i

CTidfactoraccumulate1

2521

1*11001

Where:

• π = product; • Ti = SELIC RATE or DI day (% per annum); • ∆C = percentage of the SELIC pro rata DI; • i = SELIC RATE or DI;

18

Step 2: checking of the corrected nominal value

VNC = VI * accumulatedfactor Where:

• VNC = corrected nominal value; • VI = initial value.

9.3. For trading at 100 % of the SELIC rate or DI increased by the yearly

percentage; the updated daily calculation is performed through the following formula:

Step 1: checking the correction factor or accumulated factor

( ) ( )∏=

++=n

i

ITidfactoraccumulate1

2521

2521

1001*1001

Where:

• π = product; • Ti = SELIC Pro rata DI (% p.a.); • I = annual purchased rate;

Step 2: checking of corrected nominal value

VNC = VI * accumulated_factor

Where:


9.4. After the constant updates in the previous item the following shall

proceed:

9.4.1. Common CDBs (Classified as without anticipated redemption clause and/or daily liquidity with clause of redemption at market rate).

1. The CDBs are classified by groups of issuers who have equivalent rating:

• Risk AAA

19

• Risk AA+ • Risk AA • Risk A+ • Risk A • Risk BBB • Risk B • Risk C

2. They are separated by maturity, contemplating the following periods:

• Up to 120 consecutive days; • From 121 to 365 consecutive days; • From 366 to 720 consecutive days; • From 721 to 1086 consecutive days; • From 1087 to 1440 consecutive days; • From 1441 to 1825 consecutive days; • Longer than 1825 consecutive days.

3. Thus, within each risk group and within their respective maturity group, weekly the average is calculated weighed by frequency of all rates over the last 15 days , as seen below:

3.1. Effective trading rates at BBDTVM;

3.2. auctions (firm offers) and/or consultations made by the Markets Operation Division (weekly minimum period for receipt of rates, via Notes); and

3.3. Primary issue rates registered at Cetip (excluding information with respect to training performed by the BBDTVM).

3.3.1. The accepted Cetip rates are from the financial institutions, which have their rates calculated by BBDTVM and who do not have the clause “yes” for anticipated redemption.

4. For the purposes of expurgating information that may twist the results, there will be defined, by management area, minimum rates, which are not conceptually accepted by the BBDTVM funds, for the exclusion of outlier’s rates. The Information should be forwarded, via notes, to the pricing team monthly, or in a lesser period, when there may be some fact on the market that justifies

5. Once the average by frequency is known, the standard deviation is calculated. Both the upper and lower limit correspond to +/- 1 (one) standard deviation, creating an indicative interval (Tunnel of Rate Acceptance).

20

6. All CDBs whose rates are within the tunnel of acceptance are marked to market by their own purchase rate or by the last mark to market rate used. The CDBs whose rates are outside this Tunnel of Acceptance, are marked to market by the closest limit of the Tunnel of Acceptance.

6.1. In the absence of a Tunnel of Acceptance for some grouping (rating and term), the Asset Pricing Committee, shall determine the Tunnel of Acceptance based on existing Tunnels and/or previous Tunnels.

6.2. The Asset Pricing Committee from the BBDTVM may at any moment apply a modifier (Mod) over the frequency average, for the purposes of adjusting the rates in situations where there are extreme market conditions.

6.3. Checking the Tunnel of Rate Acceptance and consequent Mark to Market rate with a modifier (Mod):

iMtM Mod = [( µi + / - Mod ) + / - σ ]

Where: • iMtM Mod

– mark to market reference rate with a

modifier (Mod) • µi – average frequency rate


• Modifier (Mod) – determined by the Asset Pricing Committee

6.4. For banks that have credit risk calculated between AAA and BBB, but with limits are suspended, canceled or without limitation, the fees will be used the upper limit of the Tunnel Acceptance Rates of their respective risks.

6.5. Determination of the mark to market rates for the ratings (B and C):

a) Creates a curve of the rates of upper Tunnel Acceptance Rate Risk BBB, where the values to be extrapolated to the risk B and C are based on calculations of the exponential growth trend Excel;

b) This curve is a series of growth where the first initial value is multiplied by the increment to get the next value in the series. The resulting product and each subsequent product are then multiplied by the increment to generate the series;

21

c) The rates for the risk B and C are unique to each and every term and every week the rates will be recalculated.

9.4.2. CDBs Subordinates

1. The CDBs subordinates are classified by the inherent credit risk of each issuer.

2. Thus, for each issuer is calculate the rate curve based on all the rates observed for the subordinate CDBs over the last 15 (fifteen) days , as shown below:

2.1 Rates effectively traded at the BBDTVM;

2.2 Consultations made by the Market Operations Division;

2.3 Rates of primary emissions registered at the Cetip (excluding information reference to effective trading by the BBDTVM).

2.3.1. Accepted Cetip rates, are from the financial institutions that detained ratings calculated by the BBDTVM.

3. For CDBs whose term are less than or equal to 720 consecutive days, due to the absence of issued subordinate CDBs with the same period, use as “vertex” the rates of common CDBs of the same Issuer and duration.

4. Daily, the rates of the vertex of the curve will be interpolated, obtaining the individual interpolated rates for each maturity to be used by the mark to market of the CDBs.

4.1 Checking the Interpolation Rate (Linear Interpolation):

( ) ( )

( ) 112

112 i

TT

TTiii I

I +−−×−=

Where:

• Ii = Interpolated Rate

• 1i = Previous Vertex Rate

• 2i = Posterior Vertex Rate

• IT = Desired Term (in working days)

22

• 1T = Previous Vertex Term (in working days)

• 2T = Posterior Vertex Term (in working days)

5. With the absence of recent rates, the Asset Pricing Committee shall determine the rates to be used on the “vertex” of this curve.

6. The Asset Pricing Committee of the BBDTVM may apply a modifier (Mod) for the purposes of adjusting the rates in extreme situations of the market, as seen below:

iMtM Mod = ( i I

+ / - Mod )

Where:

• iMtM Mod– rate reference to the mark to market with Basis

point (Mod) • i I

– interpolated rate


9.4.3. Calculation of the Mark to Market PU

a) The mark to market PU of the common CDBs and subordinate CDBs correspond to the following:

wd

Mod

wd

iMtMi

ci

vncPUMtM

×

−

++

∆×

−

++

×=

1100

11

1100

11

252

1

252

1

Where:

• PU MtM = mark to market PU • vnc = corrected nominal value • iMtM Mod

= verified mark to market rate with a Basis

point (Mod) • bd = business days up to maturity • i = curve preceding the Selic Swap X Pre (% per annum)

or DI X Pre (% per annum) Of the BM&FBovespa • ∆C = percentage of the SELIC rate or purchased DI

Note.: On the date of acquisition of the CDB its initial price registered on the system will be at the buying PU. The effect of the mark to market may only occur on D+1.

23

9.5. The CDBs with daily liquidity, with redemption clause at purchased rate , shall be updated daily at the purchase rate.

9.6. The responsibility for attributing the value to be used as modifier (Basis

Point) of the average rate and/or informed rate is of the Asset Pricing Committee from the BBDTVM, whose deliberation is communicated to the quote Fund Controller Division.

9.7. The CDB classified at the CETIP with daily liquidity, with redemption

clause at the rate of the market, shall be submitted to the model provided in item 9.4.

9.8. Classification of the issuers of CDBs and other assets, with regard to

their risk note – rating is made by the Credit Analysis Division. Its reassessment is periodic.

9.9. If the Credit Analysis Division notes an alteration in the credit risk of an

issuer, that its rating has been moved, the Fund Controller Division shall place the issuer in this new category, with the level of premium of this new category. The administrator shall employ his best efforts to identify alterations to the credit risks of the assets, imputing to the prices such alterations.

10. Term deposit with Special Guarantee from FGC

10.1. DPGE Pos-Fixed – Indexed to SELIC rate or DI

10.1.1. Contracts for Term deposits with the Special Guarantee from FGC - DPGE have the following characteristics

a. A minimum term of twelve months and a maximum term of

thirty months for deposits, with no redemption, total or partial, before the maturity date;

b. Be the object of a specific record, up to redemption, in asset systems administered by recording and financial liquidation entities, duly authorized by the Brazilian Central Bank;

c. They are formed with a single holder, person or entity, identified by their respective federal registration number (CPF) or federal corporate number (CNPJ);

d. There is no renegotiation of the original remuneration agreed to;

24

e. The sum of DPGE I and DPGE II have guarantee by the Credit Guarantee Fund – FGC limited to R$ 20 million per holder, including principal plus interest

10.1.2. Due to the absence of an active secondary market that provides volume, rate and emitter, we use the mark to market model described below.

10.1.3. Initially calculate the corrected nominal value, which takes place through the following steps to update the daily unit prices of term deposits with special guarantee from FGC – (DPGE) contracted to a percentage of the CDI/Selic:

Step 1: Finding the correction factor or accumulated factor

( )( )1*11001_ 252

1

1

+

∆

−+= ∏=

Cifactoracumulatedn

i

Where:

• ∏ = product (Pi) • i = SELIC or DI rate day (% p.a.) • ∆C = percentage of SELIC or DI rate contracted

Step 2: finding corrected nominal value

factordaccumulatevivnc _×=

Where:

• vnc = corrected nominal value • vi = initial value

10.1.4. To negotiations conducted at 100% of fees SELIC or DI plus a percentage per year, calculating the daily update is performed through the following steps:

Step 1: Finding the correction factor or accumulated factor

( ) ( )

++= ∏=

2521

2521

11001*1001_ Iifactordaccumulate

n

i

Where:

• ∏ = product (Pi) • i = SELIC or DI rate day (% p.a.) • ∆C = percentage of SELIC or DI rate contracted

25

Step 2: finding corrected nominal value


Where:


10.1.5. After the constant updates of the above procedure is the

following:

1. For effects of classification, all DPGEs are considered as Risk AAA . 2. They are separated by maturity, contemplating the following periods:

• Up to 540 consecutive days; • From 541 to 900 consecutive days; • From 901 to 1260 consecutive days; • From 1261 to 1620 consecutive days; • Longer than 1620 consecutive days.

3. Thus, within their respective maturity dates, weekly the average is calculated weighed by frequency of all rates over the last 15 days , as seen below:

3.1. Effective trading rates at BBDTVM;

3.2. Auctions / Quotes electronic order (firm offers) and/or consultations made by the Markets Operation Division; and

3.3. Primary issue rates registered at Cetip (excluding information with respect to training performed by the BBDTVM).

4. For the purposes of expurgating information that may twist the results (rates of institutions that has no intention of delivering, but send minimum rates), there will be defined, by Asset Pricing Committee, minimum rates, for the exclusion of outlier’s rates. 5. Once the average by frequency is known, the standard deviation (SD) is calculated. Both the upper and lower limit corresponds to Confidence Interval (CI) of the t distribution, according to the formula below.

26

CI =

++−+n

t

n

t δµδµ *;

*

Where:

CI – confidence interval µµµµ - average per frequency (after removal of outliers) t - statistic t be found based on the significance level (5%) and the degree of freedom that depends on the size of the frequency (Note.: The significance level is set by the Asset Pricing Committee, which can be changed depending on conditions market) δδδδ - standard deviation n - number of observations

6. In the event that there is only one fee or just repeated fees and these rates are consistent, the Asset Pricing Committee will set the SD to be used. The Upper Limit and Lower CI match a t distribution, for the number of observations, as described in the previous item. 7. All DPGE whose rates are within the CI are marked to market by their own purchase rate or by the last mark to market rate used. The DPGE whose rates are outside this CI, are marked to market by the closest limit of the CI.

7.1 In the absence of the CI for some term, the Asset Pricing Committee shall determine the CI based on existing CI and/or previous CI.

7.2 The Asset Pricing Committee from the BBDTVM may at any moment apply a modifier (Mod) over the frequency average, for the purposes of adjusting the rates in situations where there are extreme market conditions.

7.3 Determination of Mark to Market rate with a modifier (Mod):

iMtM Mod = [( IC + / - Mod )]

Where:

• iMtM Mod– mark to market reference rate with a

modifier (Mod) • IC – Confidence Interval


27

10.1.6. The calculation of PU Mark to Market DPGE correspond to the following:

bd

bd

iMi

ci

vncPUMtM

×

−

++

∆×

−

++

×=

1100

11

1100

11

252

1

252

1

Where:

• PU MtM = UP marked to market • vnc = corrected nominal value • iM = rate found for mark to market, that is, ∆C + Spread

(credit and/or liquidity risk) • bd = business days to maturity • i = average Selic or DI rate (% per annum) • ∆C = percentage of SELIC or DI rate purchased

Note: On the date of acquisition of the DPGE its initial price registered on the system will be at the buying PU. The effect of the mark to market may only occur on D+1.

10.2. DPGE Pre-fixed

10.2.1. For effects of classification, all DPGEs shall be considered Risk AAA.

10.2.2. Pricing the pre-fixed DPGE is as follows:

+

=252

1100

bd

i

vfVP

Where:

• VP = present value • vf = future value • bd = business days to maturity

28

• i = interest rate obtained by the Swap DI rate vs. PRE from BM&FBovespa, and shall be interpolated by the system if there be no specific maturity rate for the maturity of the asset.

10.2.3. For effects of contingency, the interest curve obtained by the Swap DI rate vs. PRE of BM&F/Bovespa the information from D-1 shall be repeated in D-0.

At moments of suspension of trading (Circuit Breaker), we shall use the information provided by BM&F/Bovespa.

11. Pos-fixed Assets Indexed to SELIC or DI: CCB ra te 11.1. Bank Credit Papers – CCB indexed to the TMS or CDI are updated daily

by the following formula:

11.1.1. Contracting a percentage of the indexer:

Step 1: finding the correction factor or the accumulated factor

( )( )1*11001_ 252

1

1

+

∆

−+= ∏=

Cifactordaccumulaten

i

Where:

• ∏ = product • i = SELIC or DI Day rate (% p.a.) • ∆C = percentage of SELIC or DI rate purchased

Step 2: finding the corrected nominal value


Where:


11.1.2. Contracting at 100% of an indexer plus an annual rate:

Step 1: finding correction factor or accumulated factor

( ) ( )

++= ∏=

2521

2521

11001*1001_ Iifactoracumulated

n

i

29

Where:

• ∏ = product • i = SELIC or DI rate (% p.a.) • I = purchased annual rate


factoracumulatedvivnc _×=

Where:

• vnc = nominal corrected value • vi = initial value

11.2. The Securities Commission – CVM determines in item 1.2.1.3-a

(Evaluation Criteria and Appropriation Accounting) of the COFI that in the absence of a negotiating market for a given asset, its accounting shall be by the amount that can be obtained for another asset that is similar, at a minimum, in nature, maturity, risk and indexing.

11.3. Although theoretically, the risk of a CCB is not very different from a

debenture, there are usually less transactions taking place. In the absence of an active market for CCBs, we use a Basket of Debenture Rates published by ANBIMA (Indicative rate for D-1), to determine the market rates of CCBs, in accordance with the model described below:

11.3.1. Each CCB has its own characteristics defined at issue, such as

Rate, Maturity, Indexing etc. 11.3.2. They are classified according to the rating (Risk) of the issuer,

provided periodically by the Credit Analysis Division of this DTVM: � Risk A � Risk B � Risk C

11.3.3. Each debenture is also classified according to the risk provided

by the Credit Analysis Division of this DTVM. 11.3.4. The debentures will be checked if it meets the following

prerequisites to compose the Basket Rates that will be used for mark to market of the CCB:

a) The risk of the debenture must have the same classification as the CCB;

b) The maturity term for the debenture may not be less than the CCB and shall be at the maximum 365 calendar days from the maturity date of the CCB.

30

11.3.5. The average rate of the Debentures Basket shall be calculated for mark to market for each CCB.

� Finding average rate:

iM = N

Debenturesi n

n

in∑

=1

Where:

• iM – average rate of Basket of Debentures • i n - ANBIMA indicative rate for Debenture n

• Debentures n - Debentures that make up the

Debentures Basket • N – Total Nº of observations (quantity of Debentures

that fulfilled the prerequisites)

11.3.6. The minimum quantity to make up the Basket of Debentures shall be 02 (two) debentures.

11.3.7. In the absence of the minimum quantity of Debentures to make

up the 1st Basket of Debentures for a given CCB, we will use the purchased rate for mark to market, until it is possible to make up the Basket of Debentures.

11.3.8. Should the quantity of Debentures be less than 02 (two), the

latest average rate found shall be used for marking to market until it is possible to make up a new Basket of Debentures.

11.3.9. The minimum period for calculating the average rate shall be

daily. 11.3.10. Thus the PU marked to market for the asset shall correspond to

the following:

bd

bd

iMi

ci

vncPUMtM

×

−

++

∆×

−

++

×=

1100

11

1100

11

252

1

252

1

Where:

• PU MtM = UP marked to market • vnc = corrected nominal value • iM = average rate found for marking to market • bd = business days to maturity

31

• i = average Selic or DI rate (% per annum) • ∆C = percentage of SELIC or DI rate purchased

11.4. On the date of contracting the CCB its initial price recorded in the system shall be by the PU for purchase. The effect of mark to market shall only occur on D+1.

11.5. At each modification of the rating of the CCBs and/or the Debentures that

make up the Basket, the Fund Controller Division shall make the alteration to the pricing program.

12. Pos-fixed Assets Indexed to SELIC or DI: Financ ial Bill - LF

12.1. The Financial Bills - LF are classified into six groups of emitters holding

equivalent rating, as the equivalency table demonstrated below:

EQIVALENCE TABLE OF RATING LF

Credit Risk AAA AA+ AA AA- A+ A A- BBB+ BBB BBB-

Risk LF AAA AA+ AA A+ A BBB

12.2. They are separated by maturity, including the following deadlines: • Up to 120 consecutive days; • From 121 to 365 consecutive days; • From 366 to 540 consecutive days; • From 541 to 900 consecutive days; • From 1261 to 1620 consecutive days; • Longer than 1620 consecutive days.

12.3. Thus, within each risk group and within their respective ranges of maturity, we calculate, weekly, the average weighted by frequency of all rates over the last 15 days, as follows:

12.3.1. Effective trading rates at BBDTVM; 12.3.2. Auctions (firm offers) and/ or consultations carried out by the

Market Operations Division (weekly minimum frequency to receiving rates, via Notes); and

12.3.3. Emission rates of primary operations recorded in Cetip,

excluding the information regarding the business effected by BBDTVM, from financial institutions holding the rating calculated by BBDTVM

.

32

12.4. In order to purge information that may distort the result, the area of management will determine minimum rates, which are not conceptually accepted by BBDTVM funds, for the exclusion of outliers rates. The information should be sent, via notes, to the Pricing Team, whenever there is some fact on the market that justifies it.

12.5. Once the average by frequency is known, the standard deviation is

calculated. The Upper and Lower limit correspond to +/- 1 (one) standard deviation, creating a indication interval (Tunnel of Rate Acceptance).

12.6. All LF whose rates are within the Tunnel of Acceptance are marked to

market by their own purchase rate or by the last mark to market rate used. The LF whose rates are out of that Tunnel of Acceptance, are marked to market by the closest limit of the Tunnel of Acceptance.

12.7. In the absence of a Tunnel Acceptance for some grouping (rating and

term), the Asset Pricing Committee, will determine the Tunnel of Acceptance based on the existing tunnels and/or previous Tunnels.

12.8. Given the restriction of a minimum term of 24 months for the issuance of

LF, to the tunnels acceptance below of 541consecuive days, will be used the rates of tunnels of CDB with approximate duration, plus spread defined by the Committee.

12.9. The Asset Pricing Committee of BBDTVM anytime can apply a modifier

(Mod) on the average by frequency, in order to adjust the rates in extreme market situations.

12.10. Determination the Tunnel of Rate Acceptance and consequent Mark to

Market rate with the modifier (Mod):

iMtM Mod = [( µi + / - Mod ) + / - σ ]

Where: • iMtM Mod

– mark to market reference rate with the modifier




12.11. If there is degradation of the issuers rating for LF classified as risk BBB

to an inferior risk, a mark to market risk for the issuer itself shall be adopted. Thus, there will be a check over the last 15 (fifteen) days to see whether there were trading by this issuer at Cetip. If so, assets will be priced at the rate observed in Cetip, if not, the Pricing Committee will determine a modifier to be applied to the last asset pricing rate.

33

12.12. The LF are updated daily by the following formulas:

12.12.1. Hiring a percentage of the índex:

Step 1: determination of the correction factor or cumulative factor

( )( )1*11001_ 252

1

1

+

∆

−+= ∏=


i

Where:

• ∏ = product

• i = SELIC rate or DI day (% per annum);

• ∆C = percentage of SELIC rate or DI

Step 2: determination of the nominal value corrected

factordaccumulateivnvc _×=

Where:

• nvc = nominal value correct

• iv = initial value

12.12.2. Hiring 100% of an index plus an annual rate:

Step 1: determination of the correction factor or accumulated factor

( ) ( )

++= ∏=

2521

2521


n

i

Where:

• ∏ = product


• I = contracted annual rate


34


Where:

• nvc = nominal value corrected


12.13. Calculation of PU Mark to Market :

12.13.1. The PU marked to market of LF correspond to the following:

bd

Mod

bd

iMtMi

ci

vncPUMtM

×

−

++

∆×

−

++

×=

1100

11

1100

11

252

1

252

1

Where:

• PU MtM = PU marked to market


• iMtM Mod= rate found for mark to market with the modifier

(Mod) • bd = business days to maturity • i = curve from Swap Selic X Pre (% per annum) or DI X Pre

(% py) from BM&FBovespa with Duration about 30 days (moving average of the last 10 business days)

• ∆C = Selic rate percentage or contracted DI

Note: On the date of acquisition of LF its starting price of record in the system is by purchase PU. The effect of marking to market only occurs on D +1.

12.14. The Subordinated Financial Bills – LFS are a kind of bank debenture

and were created to allow stretching of bank liabilities. We use mark to market model based on the assumptions of the model MtM Financial Bills- LF.

12.15. Known the average frequency of the Financial Bills - LF, it is applied to

the Subordinated Financial Bills one Fixed Spread due to the subordination of the paper and a Variable Spread by the period in progress. These spreads are set by the Pricing Committee of Assets of BB DTVM.

35

12.16. We use the term of 7 years as a reference to the variable spread proportional to the period.

12.17. The Pricing Committee of Assets of BB DTVM may assign modifier (Mod) to the ratings, deadlines and / or issuers in order to better suit pricing to current market conditions and the issuer when understand that the model is not full capture the risks.

12.18. The LFS are updated daily by the following formulas:

12.18.1. Hiring a percentage of the index:


( )( )1*11001_ 252

1

1

+

∆

−+= ∏=


i

Where:

• ∏ = product





Where:





( ) ( )

++= ∏=

2521

2521


n

i

Where:

• ∏ = product

36





Where:




12.19.1. Periodic payment of income – Calculation of PU Mark to Market of the asset is the sum of the payments of interest and principal, discounted (discounted to present value) by Mark to Market rate plus the modifier (Mod), according to the following formulas:

a) Calculation of interest payments for asset based compensation

percentage of DI:

[ ( )( )bdCiXfactordaccumulateVNIxerestofPayment ]1*11001[)]1_(int__ 252

1

+

∆

−+−=

b) Calculation of interest payments for asset referenced in DI +

Spread:

( ) ( )[ ]

−

++= 11001*1001_int__ 252

du

IifactorXdaccumulateVNIxerestofPayment

c) Calculation of Unit Price Mark to Market:

∑=

+

+=

n

ibd

Mod

ii

i

iMtM

PayingincipalPaymentInterestPUMtM

1252

1100

_Pr_

Where:

• PU MtM = PU marked to market • VNI = Initial Value

37


(Mod) • bd = business days between the reference date and the next

interest payment and / or business days between the dates of each event of future interest payments

• bdi = business day to maturity • i = curve from Swap Selic X Pre (% per annum) or DI X Pre


• ∆C = Selic rate percentage or contracted DI • I = annual contracted rate

12.19.2. Payment of income at the end – For the calculation of PU Mark to Market of the asset is used the following formula:

bd

Mod

bd

iMtMi

ci

vncPUMtM

×

−

++

∆×

−

++

×=

1100

11

1100

11

252

1

252

1

Where:


• vnc = nominal value correct




• ∆C = Selic rate percentage or contracted DI 12.20. For new issues, at the date of acquisition of the asset, its initial price of

the system will record the PU purchase. The effects of marking to market only occur in D+1.

38

13. Pos-fixed Assets Indexed to SELIC or DI Rate: N CE 13.1. As a Secondary Source of mark to market – MtM of Credit Notes Export -

NCE, used in the model Credit Curves ANBIMA, extracted from the debentures Percentage DI, DI + Spread and IPCA + Spread priced daily by this association, since they reflect zero-spread structures code on the sovereign curve for different risk levels. The tool sets a benchmark for the pricing of private credit assets.

13.2. The Credit Notes Export - NCE are classified by credit risk. However,

ANBIMA, Credit Curves are only calculated for the AAA, AA and A risks (disregard the signal variations within the same scale, that is, there is no distinction between classifications: neutral, plus and minus).

13.3. To calculate the mark to market credit spreads we use ,to the risks

provided by ANBIMA (AAA, AA and A), the respective curves. For other levels of risk, until they start to be made available we use the extrapolation rule (from the Risk disclosed) constant in the following table:

Rating BB DTVM Rule

BBB Rating A + 150 base points

BB Rating A + 360 base points

B Rating A + 660 base points

CCC Rating A + 1.080 base points

CC Rating A + 1.760 base points

C Rating A + 3.010 base points

RD Rating A + 7.080 base points

13.4. From the curves disclosed by ANBIMA and the new ratings created by

extrapolation, we created the equivalence table below, which will be used to calculate the mark to market credit spreads for these new ratings:

TABLE OF EQUIVALENCE OF CLASSIFICATION RISK OF NCE

Credit Curve ANBIMA AAA AA A BBB* BB* B* CCC* CC* C* RD*

Risk NCE in the Model AAA AA A BBB BB B CCC CC C RD

*New ratings created by extrapolating rule.

Table 1 – Table of equivalence used in the MtM of the Credit Notes Export

13.5. Within each risk group in their respective maturity dates, daily calculate

the average of all Credit Curve rates ANBIMA the last 15 working day.

13.5.1. The Pricing Committee of Assets of BB DTVM can change the number of working days catch ANBIMA Credit curve to compose the average.

39

13.6. Known average calculate the standard deviation of credit curves ANBIMA the last three (3) months. The Upper and Lower Limit correspond to +/- 1 (one) Standard deviation, as well as an indicative range in spread (Fees Acceptance Tunnel). These intervals are transformed into DI Percentage (rate “DI” from the DI Future Interest Rate Curve BM&FBovespa).

13.6.1. The Pricing Committee of Assets of BB DTVM at any time

can apply a modifier (Mod) on the average Credit Curve ANBIMA, aiming to adjust rates in extreme market situations, as well as, you can also change the standard deviation.

13.6.2. The Pricing Committee of Assets of BB DTVM can

differentiate he individual rating of any issuer. 13.7. Daily the NCE are separated by maturity and risk contemplating the

timing and risks of Credit Curve ANBIMA. 13.8. All NCE whose rates are within the Acceptance Tunnel are marked to

market by the hiring rate or the last marking to market rate used. The NCE that their rates are out of Acceptance Tunnel, are marked to market with the closest limit Acceptance Tunnel.

13.9. Determination of Tunnel Acceptance of Exchange Rate and consequent

Mark to Market with modifier (Mod):

iMtM Mod = [( µi + / - Mod ) + / - σ ]

Where: • iMtM Mod

– mark to market reference rate with the modifier




13.10. The NCE are updated daily by the following formulas:

13.10.1. Hiring a percentage of the index:


( )( )1*11001_ 252

1

1

+

∆

−+= ∏=


i

Where:

40

• ∏ = product





Where:





( ) ( )

++= ∏=

2521

2521


n

i

Where:

• ∏ = product





Where:



41


13.11.1. Periodic payment of income – Calculation of PU Mark to Market of the asset is the sum of the payments of interest and principal, discounted (discounted to present value) by Mark to Market rate plus the modifier (Mod), according to the following formulas:

a) Calculation of interest payments for asset based compensation

percentage of DI:

[ ( )( )bdCiXfactordaccumulateVNIxerestofPayment ]1*11001[)]1_(int__ 252

1

+

∆

−+−=

b) Calculation of interest payments for asset referenced in DI +

Spread:

( ) ( ) bd

IiXfactordaccumulateVNIxerestofPayment

++−= 2521

2521

1001*1001)]1_([int__

c) Calculation of Unit Price Mark to Market:

∑=

+

+=

n

ibd

Mod

ii

i

iMtM

PayingincipalPaymentInterestPUMtM

1252

1100

_Pr_

Where:

• PU MtM = PU marked to market • VNI = Initial Value • iMtM Mod

= rate found for mark to market with the modifier

(Mod) • bd = business days between the reference date and the next

interest payment and / or business days between the dates of each event of future interest payments

• bdi = business day to maturity • i = curve from Swap Selic X Pre (% per annum) or DI X Pre


• ∆C = Selic rate percentage or contracted DI • I = annual contracted rate

42

13.11.2. Payment of income at the end – For the calculation of PU Mark to Market of the asset is used the following formula:

bd

Mod

bd

iMtMi

ci

vncPUMtM

×

−

++

∆×

−

++

×=

1100

11

1100

11

252

1

252

1

Where:


• vnc = nominal value correct




• ∆C = Selic rate percentage or contracted DI

13.12. For new acquisitions, its starting price record in the system will be the PU

or purchase quotation. The effects of marking to market only occur on T+1.

14. Other Pos-fixed Assets Indexed to SELIC or DI R ate 14.1. In the absence of an active secondary market that provides volume, rates

and issuers we use the credit risk spread and/or premium defined in the act of purchase of the asset to price it

14.2. The Corrected Nominal Value is calculated following these steps for an

asset purchased at a percentage of the CDI/SELIC rate:


( )( )∏

=

+

∆

−+=n

i

CTifactordaccumulate1

2521

1*11001_

Where:

• π = product; • Ti = SELIC or DI Day rate (% per annum); • ∆C = percentage of SELIC or DI rate;

43

• i = SELIC or DI rate; Step 2: finding the corrected nominal value

VNC = VI * accumulated factor Where:


14.3. For negotiations effected at 100% of the SELIC or DI rate with the

addition of an annual percentage, the daily updating calculation is effected by the formula:


( ) ( )∏=

++=n

i

ITifactordaccumulate1

2521

2521

1001*1001_

Where: • π = product; • Ti = SELIC or DI rate (% per annum); • I = annual rate purchased;


VNC = VI * accumulated factor

Where:

• VNC = corrected nominal value • Corrected nominal value; • VI = initial value.

14.4. Classification of issuers for risk - rating is done by the Credit Analysis

Division. Its reevaluation is done periodically. 14.5. If the Credit Analysis Division finds an alteration in the credit risk of an

issuer, in which its rating has changed, the Fund Controller Division shall place the issuer in the new category, with the Premium level of this category. The administrator shall use the best efforts to identify the credit risk alterations for the assets, imputing prices to these alterations.

14.6. Reclassification of the issuer of other private securities into other risk

categories shall result in alteration to the spread.

44

15. Mortgage Bills – LH 15.1. Characteristics:

15.1.1. Time term: defined when effecting the operation; 15.1.2. Modality: negotiable;

15.1.3. Form of launching: public offer or direct launching in favor of the interested party;

15.1.4. Nominal value at base date: defined at purchase;

15.1.5. Updating nominal value: variation of IGP-M from the base date of the security2;

15.1.6. Interest: defined as a percentage per annum when effecting the operation based on 360 days;

15.1.7. Payment of Interest: periodicity is defined when launching the asset;

15.1.8. Withdrawal of principal: in one lump sum, on the date of maturity, by the nominal value indexed by the IGP-M, or in accordance with the criteria defined when launching the asset;

15.1.9. Updating the nominal value: by the General Price Index - Market - IGP-M of the previous month, published by the Fundação Getúlio Vargas (FGV), from the base date of the security

15.2. Methodology

15.2.1. Updating the nominal value:

−−=

MfIGP

MfIGPvnvna 1*

Where:

• vna = corrected nominal value; • vn = nominal issue value; • fIGP-M1 = month factor of the IGP-M published by the FGV; • fIGP-M = IGP-M factor in issuing the paper, published by the

FGV.

15.2.2. Updating of nominal value outside its base date or anniversary:

( )BDt

BD

MpIGPVnVna2

−=

45

Where:

• Vna = Present nominal value; • Vn = Nominal value on the date of its anniversary; • IGP-Mp = IGP-M index to be used; • BDt = business days - total in month; • BD2 = business days from the 1st of the month to the present

day.

15.2.3. Calculation of interest coupons, base of 360 days:

11100

360

30*

−

+=NMeses

ix

Where:

• x = +interest to be paid on the date; • i = interest rate on asset; • Nmeses = number of months between payments of

subsequent interest.

15.2.4. Calculation of market price:

( )vna

TIRTIR

cPULH

dctn

n

jdct

j *1

100

)1(365

1 365

++

+= ∑

=j

Where:

• PU LH = market price of Mortgage Bill; • Cj = interest coupons to be paid on the date; • Dctj/dctn = calendar days between the Day of calculation and

the date of payment of the coupon j-th (1 ≤ j ≤ n); • i = internal return rate.

15.3. Source:

� IGP-M: it is used the average calculated by the ANBIMA Macroeconomic Accompaniment Commission for the month, excepting the day following publishing of the final IGP-M, in which case the index for the current month is used, published by the FGV.

2 There are Mortgage Bills with nominal values updated by other indexes. In this manual we are dealing

only with assets indexed to the price index.

46

� TIR: are used the TIRs of the NTN-C for equivalent maturities with the addition of the Credit Risk spread, checked with the ANBIMA Table, in the column for indicative rates.

16. Private securities indexed to the IPCA – CDB, D PGEs

and Financial Bill - LF 16.1. Due to the absence of an active secondary market that provides volume,

rate and emitter for private securities indexed to the IPCA (CDB, DPGEs and Financial Bill), we elaborated model of mark to market based on the Term Structure of Interest Rates - ETTJ provided by ANBIMA, where the sovereign yield curve zero-coupon are extracted from the pre-fixed exchange rate government federal bonds and linked to the IPCA, in addition to the implied inflation in curve.

16.2. Initially calculate the Nominal Value Updated:

−−=

AfIPC

AfIPCVNEVNA 1*

Where:

• VNA = Nominal Value Updated; • VNE = Face Value Issue; • fIPC-A1 = month IPC-A factor released by IBGE; • fIPC-A = IPCA factor in the issued of the role released by

IBGE, or new upgraded factor pro-rata business days, in case of issued in different day that released by the IBGE.

16.3. If necessary, updates the Nominal Value to outside the base date or

anniversary, as follows:

( )DUt

DU

ApIPCVNVNA2

−=

Where: • VNA = Nominal Value Updated; • VN = Nominal Value at the date of the anniversary; • IPC-Ap = IPCA index to be used (last index); • DUT = Number of business days ranging from the 15th of the previous month to the 15th of the current month; • DU2 = Number of business days ranging from the 15th of the previous month to the current day

16.4. The calculation of PU PAR corresponds to the VNA plus interest of the

paper, according to the following formulas:

47

+= 1100

InterestVNAPUPAR

1001100

Xi

InterestN

n

−

=

( )

=100

aymentInterest_pInterest

XVNA

Where:

• i = Interest as a percentage per year; • N = number of days representative of the rate, that may take the values 360 or 365 consecutive days or 252 business days; • n = When "N" is equal to 360 or 365 days, "n" will assume the number of days between the date of the next event and the date of the previous event. When "N" is equal to 252 days, "n" will assume the number of days between the date of the next event and the date of the previous event.

16.5. The calculation of PU Mark to Market of the asset is the sum of the

payments of principal and interest, discounted (discounted to present value) for the interpolated Term Structure of Interest Rates - ETTJ IPCA, provided by ANBIMA, plus the Credit Spread, according to the following formula:

∑=

++

+=n

idu

ii

i

Spread

paymentincipalPUMtM

1252

1100

rate edInterpolat

_PraymentInterest_p

Where: • PU MtM = PU mark to market • du = business days to maturity • Interpolated rate = Exponential Interpolation of ETTJ IPCA • Spread = Credit Spread (date of issue)

16.6. For new issues, at the acquisition date of the asset, its initial register

price in the system will be the purchase PU. The effects of mark to market only occur on T+1.

48

16.7. If there is change in issuer risk, the Committee of Asset Pricing of BBDTVM reassess its respective Credit Spread

16.8. In a contingency situation will be used to structure ETTJ Estimated, provided by ANBIMA on T-1.

17. Certificates of Real Estate Receivables - CRI 17.1. BM&FBovespa there is the closing reference Price (PRF) of BOVESPA

FIX, which is the result of a process of price formation with clear and transparent rules of trading, as Reference Price Manual of Debentures. This pricing, coupled with the transparency provided by the system – once the offerings, business and closing prices are spread throughout the market in real time – allows you to use the PRF to the Mark to Market – MtM of CRIs.

17.1.1. Use the MtM of CRIs mode Referential price settlement to T+ 0. 17.1.2. In cases where no prices (such as a holiday in SP Square) will

be used the T-1 Reference Price MtM settlement mode to T+1. 17.1.3. In contingency situation MtM update the Unit Price of the DI-

Cetip rate. 17.1.4. The BB DTVM Asset Pricing Committee at any time may act as

fashion model to correct any distortions that occur.

17.2. For new purchases, the date of acquisition of CRI, its starting price record in the system will be through the purchase PU. The effect of marking to market only occurs on T+1. 17.2.1. The assets that may BM&FBovespa not priced will be handled

by the Pricing Committee of Asset of BB DTVM.

49

E - ASSETS NEGOTIATED ABROAD

18. ADR – American Depositary Receipt 18.1. Mark to market of assets negotiated in the New York Stock Exchange

(NYSE) shall take place through the so-called “latest price” published by the systems, but not necessarily meaning the last effective transaction.

18.2. We use as a parameter of the prices captured and time to capture international asset prices, the closing of the NYSE. If there is no trading we repeat the quotes recorded on the last working day;

18.3. On the 24th and 31st of December, prices will be captured in Bloomberg, at 14h (GMT).

18.4. If there is no trading is kept the “last price” as published by the systems

on the previous day. 18.5. The exchange rate for conversion to foreign currencies to the domestic

currency portfolio of foreign debt investment funds is performed using the Ptax800, sales closing price.

18.6. The exchange rate for conversion to foreign currencies into the national

currency in mark-to-market portfolio of investment funds is performed using the Exchange Rate Reference T2 calculated by BM&FBovespa.

18.7. Source: CMA, BROADCAST, BM&FBovespa and BLOOMBERG.

19. Fixed Income – Corporate Bonds, Treasury Bonds,

Global, CLN, etc. 19.1. The mark to market of fixed income assets traded abroad is done taking

as a basis offers of quotations published by CMA, BROADCAST and BLOOMBERG.

19.2. We use as a parameter of the prices captured and time to capture

international asset prices, the closing of the NYSE. If there is no trading we repeat the quotes recorded on the last working day;

19.3. On the 24th and 31st of December, prices will be captured in Bloomberg, at 14h (GMT).

50

19.4. The exchange rate for conversion to foreign currencies to the domestic currency portfolio of foreign debt investment funds is performed using the Ptax800, sales closing price.

19.5. The exchange rate for conversion to foreign currencies into the national

currency in mark-to-market portfolio of investment funds is performed using the Exchange Rate Reference T2 calculated by BM&FBovespa.

19.6. Source: CMA, BROADCAST, BM&FBovespa and BLOOMBERG.

F- VARIABLE INCOME AND FUTURES

20. Shares and BDRs – Brazilian Depositary Receipts

20.1. Mark to market of assets traded in the stock market shall be by the closing price published by BM&FBOVESPA.

20.2. The Brazilian Depositary Receipt – BDR (level II and III) is marked to

market at the closing price published by BM&FBOVESPA. 20.3. If there is no negotiation is held the previous day’s closing price, or in

accordance with current law.

20.4. For BDR Sponsored Level I, the mark to market will be given by the reference value established by BM&FBOVESPA.

20.5. There is no disclosure of the reference value, is held the last available value.

20.6. Source: BM&FBOVESPA

21. Subscription Rights and Receipts of Shares

21.1. In the period between the day on which the shares become ex-subscription and the day for the beginning of trading of the right, the price of the Subscription Rights will be calculated using the Black & Scholes model, the same as a call option, as the following parameters:

C= ( ) ( )2

t r10 dNeEdNS ⋅⋅−⋅ ⋅

d1 = t

trES

.

).2/()/ln( 20

∂∂++

51

d2 = t

trES

.

).2/()/ln( 20

∂∂−+

= d1 - ∂ . t

Where:

• C - value of subscription rights • r - Interest rate without risk • S0 - Price (closing) of the asset to which the right relates • E - Exercise price, which will be the subscription price of the share

to which it refers • t - remaining period to the date of subscription right • N (d1) N (d2) - value of the cumulative normal distribution

evaluated at point d1 and d2 • σ - volatility of the returns of the underlying asset, which the right

refers.

21.2. From the moment the Subscription Rights starts to be traded, the market price shall be the closing price of the business conducted and published by BM & F Bovespa.

21.3. If, in the negotiation period, the right has become illiquid, will be maintained the closing price of the previous day.

21.4. The market price of the Subscription Receipt is the closing share price at

which the receipt refers. 21.5. Source: BM&F/BOVESPA

22. Rent (or loans) of Shares

22.1. For pricing of rent (or loan) shares the contract rate is used, because the operation has guarantee from CBLC and the possibility of early redemption to the contracted rate.

23. Futures BM&F/BOVESPA

23.1. Future contracts traded in the BM&F/BOVESPA have standardized characteristics of value, maturity, minimum contracts and adjustment prices. For purposes of daily updating, quotes or values are used for the day´s adjustment price.

23.2. For contingency purpose, or even as an alternative form of pricing, for

assets that have BM&F/BOVESPA as their main source of indexes, the information of D-1 shall be repeated for D-0.

52

23.3. At moments of suspension of trading (Circuit Breaker), we will use the information supplied by BM&FBovespa itself.

23.4. Source: BM&F/BOVESPA 24. SWAP 24.1. The operation consists in an exchange of rentability referenced to a given

notional value between two parts through daily adjustments in cash flow. 24.2. The flows are updated by daily adjustments, keeping a direct correlation

with the business updated to the market. For example, a swap of pre rates against CDIs the rentabilities adjust to one another, and maintain their value positions in the market.

24.3. Adjustment of positions is provided daily by BM&F/BOVESPA. 24.4. For effects of contingency, or even as an alternative way of pricing, for

assets that have BM&F/BOVESPA as the primary source of indexes, the information on D-1 shall be repeated on D-0.

24.5. At moments of suspension of trading (Circuit Breaker), we will use the

information supplied by BM&FBovespa itself. 24.6. Source: BM&F/BOVESPA. 24.7. Below we describe the methodology for specific calculations for swap

operations – Exchange leg:

Step 1: Calculation of Principal

=

yDtECotCurrenc

yDtCotCurrencxVEPa

0

Where:

• Pa= updated principal • VE = value of issue in Reais • CotCurrencyDt0 = quotation of Currency x R$ for the day of

calculation • CotCurrencyDtE = quotation Currency x R$ date of issue

Step 2: Calculation of interest

53

PaXBD

BDX

couponJ

E

= 0

100

Where:

• J = interest • BD0 = business days between date of issue and date of

calculation • WDE = business days between date of issue and maturity of

contract

• ( )

=360

.% CCDXannunperagreedratecoupon , where CDC is the

number of calendar days of the contract

• Pa = updated principal

Step 3: Calculation of Foreign Exchange leg

Exchange leg = Principal + Interest 25. Options

25.1. Liquid Options

Closing price quotes from BM&F/BOVESPA are used for options with liquidity.

Source: BM&F/BOVESPA.

25.2. Low Liquidity Options

For options with low liquidity we use the Black & Scholes model for pricing, where the source of calculation of volatility is the historic series3 of prices of shares from BM&F/BOVESPA.

⇒ BLACK & SCHOLES MODEL

C=S 0 . N ( d1 ) – E . e- r.t . N ( d2 ) - equation 1

3 For index options will be used the implied volatility, found through the smile curve of the options that

were quoted on the stock exchange. In the impossibility of constructing the curve, will be used volatility captured at Bloomberg.

54

P=E . e- r.t . N (-d2) - S 0 . N (-d1) ou P = C - S 0 + E . e-i.t - equation 2

d1 = t

trES

.

).2/()/ln( 20

∂∂++

- equation 3

d2 = t

trES

.

).2/()/ln( 20

∂∂−+

= d1 - ∂ . t - equation 4

Variables involved in the model

• r – interest rate without risk

• C or P – current value of option

• S0 – current price of share to which the option refers

• E - exercise price of the option

• t – remaining price after option

• ∂ – volatility of returns from asset that is the object of the option

• N(d1) , N(d2) – value of normal accumulated distribution, evaluated at

point d1 , d2

Calculation of historical volatility ∂

Based on a sample of 21 latest prices of the asset we define the relation

ln 1−i

i

p

p

Where:

• Pi – closing price from stock market at date i

• Pi-1 – closing price from stock market at date i – 1

Then, the standard deviation is calculated for the results, multiplied by

252 giving the annualized volatility.

55

The function N(d) is the accumulated probability function of a normal standardized variable, that is, the probability that a variable with a standard normal distribution, φ (0 , 1), is less than d.

25.3. Barrier Options

\We use the model developed by Merton, Reiner and Rubinstein.

⇒ MERTON (1973) E REINER E RUBINSTEIN (1991) MODEL

Compiled by ESPEN GAARDER HAUG, The Complete Guide To Option Pricing Formulas – Second Edition, 2007.

Exotic Options with Barriers Conventions: � Options with knock in barriers – The option only exists if the barrier

is reached during the life of the contract. � Options with knock out barriers – the option no longer exists if the

barrier is reached during the life of the contract, which might or might not have a rebate.

� When a barrier is defined with a value above the current price of the

asset, it is called Up and In (UI) and when reaching the barrier the right becomes available. Up and out, (UO) in this case, when the barrier is reached the right no longer exists.

� Similarly, when the barrier is established at an amount lower than

the current price of the asset, it is said that the option is Down and IN (DI) or Down and OUT” (DO).

� Rebate: the amount to be paid to one of the parties when the barrier

is reached, represented by a pre rate, not to be confused with the asset in question.

� Volatility: historic volatility, annualized, as described in the Black &

Scholes model, with the use of a sample of 21 days.

A = ( ) ( ),11 _)( TxNXexNSe rTTrb φσφφφφ −−− B = ( ) ( ),22 _)( TxNXexNSe rTTrb φσφφφφ −−−

56

C = ( )

( ) ( )( ),112

_12

)( TyNS

HXeyN

S

HSe rTTrb ησηφηφ

µµ

−

−

+

−

D = ( )

( ) ( )( ),222

_12

)( TyNS

HXeyN

S

HSe rTTrb ησηφηφ

µµ

−

−

+

−

E = ( ) ( )( ) ,222

−

−−− TyNS

HTxNKe rT ησηση

µ

F = ( ) ( )( ) ,2..

−

+

−+

TzNS

HzN

S

HK ηλσηη

λµλµ

Where:

• x1 = ( ) ( ) T

T

XS σµσ

++ 1ln

• x2 = ( ) ( ) T

T

HS σµσ

++ 1ln

• y1 = ( ) ( ) T

T

SXH σµσ

++ 1ln 2

• y2 = ( ) ( ) T

T

SH σµσ

++ 1ln

• z = ( )

TT

SH λσσ

+ln

• µ = 2

2 2

σσ−b

• λ = 2

2 2

σµ r+

Where: • S = Spot price of the asset • X = exercise price of the option • H = barrier price of the option • T = option expiration • K = value of rebate

57

• σ = volatility of the option • b = cost of carrying • r = pre-fixed rate • n, Φ = parameters for specific models for each kind of option which

can be 1 or -1

Options with Knock-in barrier clauses:

Options with barrier clauses are divided into Knock-in and Knock-out. In the first the right to exercise only begins to exist if the price of the asset S reaches the price of the barrier before the maturity date T. Knock-in options are classified as in-and-down (S > H), that is, spot price greater than barrier or in-and-up (S < H), that is, spot price lower than the barrier. See following:

� Knock-in-and-down – indicates that the price of the asset on the

date of launching is above the price of the barrier, that is S > H. The payoff of the option is given by:

� Call: pay-off = Max(S – X; 0) if S ≤ H before maturity T and pay-off –

K (rebate), otherwise; � Put: pay-off = Max(X – S; 0) if S ≤ H before maturity T and pay-off

– K (rebate), otherwise;

The formulae for calculating the premiums for these options are obtained from the combination of the variables previously described, such as A, B, C, D, E, and F, as established by the model, that is:

Call in – and – down (X > H) C + E η = 1, Φ = 1

Call in – and – down (X < H) A – B + D + E η = 1, Φ = 1

Put in – and – down (X > H) B – C + D + E η = 1, Φ = -1 Put in – and – down (X < H) A + E η = 1, Φ = -1

� Knock-in-and-up – indicates that the price of the asset on the date of launching the option is below the barrier price, that is, S < H. The payoff for the option is given by:

� Call: pay-off = Max(S – X; 0) if S ≥ H before maturity T and pay-off –

K (rebate), otherwise; � Put: pay-off = Max(X – S; 0) if S ≥ H before maturity T and pay-off

– K (rebate), otherwise;

58

The formulae for calculation of the premiums are given by the sum of the following variables:

Call in – and –up (X > H) = A + E η = -1, Φ = 1

Call in – and – up (X < H) = B – C + D + E η = -1, Φ = 1 Put in – and – up (X > H) = A – B + D + E η = -1, Φ = -1 Put in – and – up (X < H) = C + E η = -1, Φ = -1

Options with Knock-out clauses:

Options with Knock-out barrier clauses are very similar to traditional options, except that no longer exist if the underlying asset price S reaches the knock-out barrier before the maturity date. Similarly to the options with Knock-in barriers, there is a prerogative of a rebate (K), which is paid if the option no longer exist before maturity. The Knock-out barrier may be either out-and-down or out-and-up. The payoff and the premium are calculated as shown below:

� Knock-out-and-down – indicates that the price of the asset on the

date of launching of the option is above the barrier price, that is, S > H. The payoff for the option is given by:

� Call: pay-off = Max (S – X; 0) if S > H before maturity T and pay-off =

K (rebate),otherwise; � Put: pay-off = Max (X – S; 0) if S > H before maturity T and pay-off =

K (rebate),otherwise;

The formulas for calculating the premium for these options are obtained by a combination of variables described above, such as A, B, C, D, E, and F, as established by the model below:

Call out – and – down (X > H) = A – C + F η = 1, Φ = 1

Call out – and – down (X < H) = B – D + F η = 1, Φ = 1

Put out – and – down (X > H) = A – B + C – D + F η = 1, Φ = -1 Put out – and – down (X < H) = F η = 1, Φ = -1

59

� Knock-out-and-up – indicates that the price of the asset on the date of launching of the option is below the price of the barrier, that is, S < H. The payoff for the option is given by:

� Call: pay-off = Max (S – X; 0) if S < H before maturity T and pay-off =

K (rebate),otherwise; � Put: pay-off = Max (X – S; 0) if S < H before maturity T and pay-off

= K (rebate), otherwise;

The formulae for calculation of the premium are given by application of the sum of the following variables:

Call out – and – up (X > H) = F η = -1, Φ = 1

Call out – and – up (X < H) = A – B + C – D + F η = -1, Φ = 1

Put out – and – up (X > H) = B – D + F η = -1, Φ = -1 Put out – and – up (X < H) = A – C + F η = -1, Φ = -1

25.4. Futures Options

Index Options, Dollar Options, IDI Options and DI Futures Options. Used the averages of trades published by BM&F/Bovespa for the options that have liquidity. � In the absence of trading on the day, will be used the Reference

Premium daily disclosed by BM&F/Bovespa for these assets.

� If the BM&F Bovespa disclose the Premium Reference after limit time for dispatch the prices to Funds Processing area, the options are priced through the Black model (1976), detailed below:

⇒ BLACK MODEL

Call

( ) ( )[ ]21 dNKdNFec nrT ⋅−⋅= −

Put

( ) ( )[ ]12 dNFdNKep nrT −⋅−−⋅= −

60

With

T

TKFd n

σσ ).2/()/ln( 2

1

+=

TdT

TKFd n σ

σσ −=−= 1

2

2

).2/()/ln(

Where:

• c – price of a purchase option;

• p – price of a European sales option;

• K – exercise price or rate for exercising expressed in PU in the

case of options on DI futures;

• rd – pre interpolated rate (interest rate without risk);

• r – rate of continuous time defined as being equal to ln (1+ rd);

• σ – implied volatility;

• T – time in years ( )252nbd ;

• nbd – number of business days between the date of D0 and the

maturity of the option;

• N(.) – Accumulated distribution function of the standard normal;

• nF – Price of adjustment of futures contracts as bellow:

1F - Price of adjustment of index futures contract of maturity

equal to the maturity of the option;

2F - Price of adjustment of futures contract for the dollar at

maturity equal to maturity of the option;

3F - Price of adjustment of futures contract for IDI, where:

sa

F *000.100

3 =

Where:

• s: IDI on the date of calculation

61

• a: price of adjustment of futures contract for DI of 1 day

of maturity equal to maturity of the option

4F - Forward rate expressed in PU between the maturity of the

option on the Future DI and the term according to the kind of

option.

Where:

b

aF

000.1004 =

Where:

• a: price of adjustment of the DI futures contract of the 1 day, of maturity equal to maturity of the option.

• b: price of adjustment of the DI futures contract

of the 1 day, of maturity equal to maturity plus the term of the agreement, according to the type of option.

25.4.1 For the Option on the DI futures we have:

a) The underlying asset of the option is the forward rate of three (type A), six (type B) or twelve months (type C) from the maturity of the option.

b) Given that a European CALL for DI futures is equivalent

to a European PUT of futures PU for DI; a European PUT for futures rate of DI is equivalent to European CALL for PU of futures DI, the price of a CALL is determined by PUT for futures rate of DI and vice-versa.

25.4.2 The volatility to be applied to Black model, will be the implied volatility derived from the D-1 Premium Reference of BM&F Bovespa.

25.4.3 In the absence of Premium Reference published by the BM&F

Bovespa, or if the data is considered inconsistent/distorted, the volatility is calculated using a basket of implied volatilities (Smile Volatility) of the options that had business listed on stock

62

25.4.4 In the absence of data for the construction of smile volatility or, if the data are distorted or incomplete, should be used the market volatility captured on the Bloomberg terminal.

25.4.5 Failing to apply the proposed models, shall be used in an

emergency/contingency situation, the price set on the day before.

25.4.6 Exceptionally, in extreme market circumstances, the Pricing

Committee of BBDTVM may establish additional criteria for the use of secondary methods, in order to better reflect the reality of the market, recording such criteria in the minutes.

25.5. Foreign Currency Options

For mark to market of options on foreign currencies, will be used prices disclosed daily by BM&F/Bovespa.

� In the absence of trading on the day, will be used the Reference Premium daily disclosed by BM&F/Bovespa for these assets.

� If the BM&F Bovespa disclose the Premium Reference after limit time

for dispatch the prices to Funds Processing area, the options are priced through the Garman-Kohlhagen model (1983), detailed below:

⇒ GARMAN-KOHLHAGEN MODEL

Call

( ) ( )21 dNeKdNSec rTTrc ⋅⋅−⋅⋅= −−

Put

( ) ( )12 dNSedNeKp TrrT c −⋅⋅−−⋅⋅= −−

With

T

TrrKSd c

σσ ).2/()/ln( 2

1

+−+=

63

TdT

TrrKSd c σ

σσ

−=+−−

= 1

2

2

).2/()/ln(

Where:

• c – call option premium (purchase option);

• p – put option premium (sales option);

• e – irrational number called Euler number of value of approximately 2.718281828459045;

• K – exercise price of the option;

• S – spot price of the underlying asset;

• r – interest rate without risk (pre-interpolated rate);

• rc –external interest rate free of risk;

• σ – volatility of asset;

• T – time in years for maturity of contract;

• nbd – number of business days between date of D0 and maturity of the option;

• N(.) – Accumulated distribution function of standard normal;

25.5.1 The volatility to be applied to Garman-Kohlhagen model will be

the implied volatility derived from the D-1 Premium Reference

of BM&F/Bovespa.

25.5.2 In the absence of Premium Reference published by the

BM&F/Bovespa, or if the data is considered

inconsistent/distorted, the volatility is calculated using a basket

of implied volatilities (Smile Volatility) of the options that had

business listed on stock.

25.5.3 In the absence of data for the construction of smile volatility or,

if the data are distorted or incomplete, should be used the

market volatility captured on the Bloomberg terminal.

25.5.4 Failing to apply the proposed models shall be used in an

emergency/contingency situation, the price set on the day

before.

64

25.5.5 Exceptionally, in extreme market circumstances, the Pricing

Committee of BBDTVM may establish additional criteria for the

use of secondary methods, in order to better reflect the reality

of the market, recording such criteria in the minutes.

26. Exotic Options

26.1. QUANTO Adjustment

Described in detail by Shreve (2004) and Hull (2000) – captures the fact that an option is referenced to an index quoted in a foreign currency, while its settlement is made in another currency, in this case the domestic currency, the Real. The Quanto considers the currency in which the object of the option is quoted and the currency in which the option is quoted.

The Quanto Adjustment takes into consideration the following variables in its calculation: Implied Volatility of the underlying Asset (External Index); Implied Volatility of the Exchange Rate - Real x foreign exchange - (settlement); the correlation between the returns of the Index and the Exchange Rate – Real x Foreign exchange and the number of days to maturity of the option, in accordance with the formula below:

( )tAdjustmentQuanto ***exp ηϕσ=

Where:

• σ = Implied Volatility of the underlying Asset (External Index) • ϕ = Implied Volatility of the Exchange Rate Real x Foreign exchange

• η = Correlation between the return index and the exchange rate

• t = number of days to the maturity of the Option

The Implied Volatilities used for the purposes of this calculation may not be directly observed, as such, shall be calculated through trial and error4 (Solver tool in Excel). We detail below the Implied Volatility calculation:

a) The historical Volatilities are captured on Bloomberg, through the

function GV (Graph Volatility) function, from the respectives international indexes and exchange rate between Real x Foreign

4 Course “Qualifying Professionals for the Derivatives Market – BM&F – Mar2007”.

65

currency, for a period up to the maturity term of the operation (the term depends on the conditions of the market at the moment of calculation);

b) The Implied volatility is then regarded as the volatility that balances

the premium supplied by the calculation agent 5 with the theoretical premium calculated by the pricing model of the Option, obtained through the application of the Excel Solver tool in the Historic Volatilities..

The Correlation, also called the Correlation Coefficient, indicates the force and direction of the linear relationship between the variables weekly return on underlying asset and weekly return on exchange rate Real x Foreign currency. Its value is always between -1 and 1, where 0 means no correlation. The positive value means a positive relation between the variables, while the negative value means the very opposite direction (on average). The higher the value of the correlation (positive or negative), the stronger the Association.

The equation for the Correlation Coefficient is:

( )yx

yx

YXCov

σσρ

⋅=

,,

Where X and Y are the average samples of the variable matrixes; Cov is the co-variance and yx e σσ are the standard deviations of the samples.

� The calculation of the Correlation is made directly by Excel Correl

Function. � The Return is calculated on a weekly basis in order to expurgate

time differences at the close of the indexes and exchange rates Real x Foreign currency.

� Obs.: The Market only consider the absolute number of correlation

for the calculation of the Quanto. The result of the Spot or Forward (depending on the Option Model used) of the International index, corrected by the Quanto Adjustment, is obtained by the formula below:

QuantoAjusteSQS *=

Where: • QS = Spot or Adjusted Forward

• S = Spot or Forward price of the International index. 5 Agent defined under contract, responsible for calculating the operation.

66

The result obtained for the QS will be the new value of the index to be employed on the pricing model for the options referred to more than one currency.

26.2. Asian Options

Asian options averages may be calculated in three different ways: geometrically (Geometric Average-Rate Options); arithmetically (Arithmetic Average-Rate Options); and discrete arithmetic (Discrete Arithmetic Average-Rate Options).

This manual deals with the discrete arithmetic of pricing (Discrete Arithmetic Average-Rate Options), together with the Quanto Adjustment, whenever necessary.

Discrete Asian Approximation (Levy, 1997 e Haug, Haug and

Margrabe, 2003)

Call

( ) ( )[ ]21 .. dNXdNFec ArT

A −≈ −

Put

( ) ( )[ ]12 ... dNFdNXep ArT

A −−−≈ −

With

T

TXFd

A

AA

σσ 2/)/ln( 2

1

+= Tdd Aσ−= 12

Where:

• cA = price of the European Asiatic call • pA = price of the European Asiatic put • X = strike • SA = average up to the present moment • S = spot • r = pre interpolated rate (interest rate without risk); • b = cost of carrying • N(.) = Accumulated distribution function of the normal standard • ln = natural logarithm base e

67

• e = is an irrational number, known as the Euler number, with approximate value equal to 2,718281828459045

• n = number of averages to be calculated • m = number of averages already calculated

• 1

1

−−=

n

tTh

• T = calendar days to maturity of the option (in years) • t1 = calendar days to run before the next average (in years) • σ = implied volatility

• Aσ = adjusted volatility

( ) ( )T

AEAE TTA

][ln2][ln 2 −=σ

• FA is defined as E[AT]

• bh

bhnbt

Te

ee

n

SAE

−−=

1

1][ 1

•

( ) ( )( ) ( )

( )( )

−−−

−−

−+

−−=

+

+

++

++

hb

hnb

bh

bhn

hbhb

hnbb

Te

e

e

e

ee

e

n

teSAE

2

2

22

22

2

2

2

2

2

222

1

1

1

1

1

2

1

11][

σ

σ

σσ

σσ

� When b=0 we have:

SAE T =][

−−−

−+

−−=

h

hn

hh

hnt

Te

en

ee

e

n

eSAE

2

2

22

22

1

1

1

2

1

1][

2

122

σ

σ

σσ

σσ

If are in the averaging period, m>0, the price of the strike should be substituted for

mn

mn

mn

mSnXX A

−−

−−

=

Moreover, if Xm

nSA > , certainly the call will be exercised and the

put will end out of the money. That is, the value of the PUT will be zero, while the value of the CALL shall be:

−=∧

− XSec ArT

A

Where:

68

n

mnAE

n

mSS AA

−+=∧

][

When we have only one price to be calculated before maturity of the option, the value can be calculated using the Black-Scholes-Merton (BSM) weighing by time remaining to maturity and adjusting

the price of the strike (∧X ). In this case, the value of the Asian

option call is:

nbrTXScc BSMA

1,,,,,

=∧

σ

Where:

• CBSM is the general formula for the BSM of the call

( ) )2()1( dNXedNSec rTTrb

BSM−− −=

• ∧X =n.X – (n-1)SA

The value of the Asian PUT is:

nbrTXSpp BSMA

1,,,,,

=∧

σ

Where:

• pBSM is the general formula for the BSM for the put

( ) )1()2( ) dNSedNXep TrbrTBSM −−−= −−

With

( )

T

TbX

S

dσ

σ 2/ln

1

2++

= Tdd σ−= 12

27. Synthetic Operations 27.1. Synthetic operations present individualized treatment at their legs. Each

asset must be submitted to its own pricing methodology. 27.2. Each asset involved in the operation has its own form of pricing as

described in this manual, independent of whether it's part of synthetic operation or not.

69

27.3. Market rates are obtained by way of an interest curve, demonstrated in

item Term Structure of Interest Rates, provided above. 27.4. Source: ANBIMA, BM&F/BOVESPA.

70

G - FIXED EARNINGS OPERATION – SHARE TERM

28. Share Term

28.1. The share term operations are considered fixed income and are similar to a pre-fixed asset, once the return rate is known at the time of the operation, as shown in the following formula:

1001

252

×

−

=bd

vi

vfi

Where: • I = rate of return • vf = future value • vi = initial value • bd=- business days from settlement to maturity

28.2. Throughout the duration of the asset, the operation risk is the interest rates, once their profitability has been defined until the end, because its similarity to a pre-fixed operation.

28.3. The pricing of this asset is calculated using the following formula:

+

=252

1100

bd

i

vfVP

Where:

• VP = present value • vf = future value • i = interest rates obtained by the Swap rate DI vs. PRE of the

BM&F/Bovespa, which should be Interpolated by the system, if there is no final rate for the asset.

• bd = business days until maturityo

28.4. For purposes of the contingency, the interest curve is obtained through the Swap rate DI vs. PRE of the BM&F/Bovespa which shall be repeated on D-0 information from D-1.

28.4.1. Whenever there is a break in trading (Circuit Breaker), we use

the informations supplied by the BM&F/Bovespa itself.

71

H – REPURCHASE AGREEMENTS

29. Repurchase Agreements

29.1. The repo operations are backed by public or private securities and are characterized by the purchase and sale of securities with resale commitment assumed by the buyer in conjunction with repurchase agreements entered into by the seller.

29.2. May be registered in the SELIC or CETIP (depending on the type of

asset).

29.3. In SELIC are four types of repos: Type 1 – Settlement of the repurchase / resell at a date predetermined (conventional operation); Type 2 – Settlement of the repurchase / resell at any time during a given period, at the discretion of either party, as previously agreed between them; Type 3 – Settlement of the repurchase / resell at a date certain deadline or within the sole discretion of the purchaser; and Type 4 – Settlement of the repurchase / resell at a date certain deadline or within the sole discretion of the seller.

29.4. In CETIP can type “repo” (sale of securities with repurchase agreements), “with repo reverse repo” (sale of securities with repurchase agreements and simultaneous purchase with resale commitment) and “reverse repo” (buying securities with resale commitment).

29.5. The rate used to price of these is the committed rate of operation.

72

I – SHARES OF FUNDS

30. Shares of Investment Funds

30.1. For funds that have shares traded is used the closing price of the business. In case there is no business for 90 days, we will use the value of the shares issued by the administrator.

30.2. For funds that do not have publicly traded shares is used the value of the

shares released by the administrator.

BBDTVM Asset Management – Distribuidora de Títulos e Valores Mobiliários S.A. Funds Controller Division – Board Solutions Wholesale – DISAT – Banco do Brasil S.A.

Rio de Janeiro (RJ)

Praça XV de Novembro, 20 – 2º e 3º andar – Centro – CEP 20010-010 #: 55-21-3808-7500 – Fax: # 55-21-3808-7600

[email protected]

São Paulo (SP) Av. Paulista 2.300 – 4º andar – Conjunto 42 – Cerqueira César – CEP 01310-300

# 55 11 2149-4300 – Fax. # 55-11-2149-43100 [email protected]

www.bb.com.br/bbdtvm

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