Credit Derivatives Pricing and Applications

Credit Default Swaps

The notional amount of credit default swap in the second half of 2007 was nearly $60 trillion, while gross market value at $2 trillion over the same period. The Y-axis on the gross market value is in basis points as the cost of buying protection (buying default insurance CDS) decreased from the 2nd half of 2004 to the first half of 2007 to about 30 bps , rising significantly after 07, due to rising foreclosure and default.

Global OTC Derivatives Market

The notional amount and gross market value of credit default swap in 2007 were over $57 trillion, and slightly over $2 trillion. The over the counter contracts OTC on interest rate products, FRAs, swaps (interest rate and currency), and options notional and gross market value in 2007 respectively was over $393.13 trillion and $7.177 trillion.

Notional V Gross Market Value Notional amounts outstanding provide a measure of market size and a

reference from which contractual payments are determined in derivatives markets. However, such amounts are not truly at risk. The amounts at risk in derivatives contracts are a function of the

1. Price level and/or volatility of the financial reference index used in the determination of contract payments,

2. The duration and liquidity of contracts, and the creditworthiness of counterparties.

3. They are also a function of whether an exchange of notional principal takes place between counterparties.

4. Gross market values provide a more accurate measure of the scale of financial risk as a measure of cost of replacing the contract.

The term “gross” is used to indicate that contracts with positive and negative replacement values with the same counterparty are not netted.

Credit Derivative Products

Credit default swap Credit linked Noted CLOs Total return swap Credit spread forward Credit spread Option

Credit Spread

The spread of default-free bond with that of the defaultable debt instruments provides valuable information in the following ways.

-Conveys Probability of default -As a leading economic indicators -As an efficient allocator

Implication of spread

Using the spread the Central Banks analyze the interdependence between:

The Treasury bonds, corporate bonds and money market debt to gain insight into responses to monetary policy changes.

For example, widening or tightening spread is the credit market response to ration credits to the less credit (good credit) worthy issuer.

Application of Credit Derivatives

Credit derivatives enable the parties to reduce credit exposure without physically removing assets from the balance sheet.

However, transaction on credit derivatives is confidential and does not require notification of the customer thereby separating fiduciary relationship with that of the risk management decisions.

Credit Event/Default Swap

This is an over the counter contract between two parties, where party A the buyer of the protection pays an annuity (insurance premium) to the party B, the seller of the protection on the risky debt instrument “reference asset” issued by party C.

Protection seller (Party B) is obligated to pay the face value of the reference asset/assets triggered by the events as outlined in the ISDA master agreement contract.

Uncorrelated conterparty

Exhibit 11.4 Credit Default Swaps Cash Flows

1 2 3 4 5

Time (Year)

US

Do

llars

Max [Par(1-R)|ISDA events, 0]

R is the average recovery rate on defaulted debt

The buyer of CDS pays the seller series of level premium, and receives Max [Par(1-R)|ISDA events, 0]. In the event the trigger event as outlined in the ISDA master agreement happens, the seller pays the buyer Par value of the bond*(1-recovery rate). If no trigger events happen, the seller makes money for assuming the expected risk.

Credit Default Swap Quotation (A1/A)

Term BidOffer Ref obligation XYZ 7.125% 1/31/ 10

5 yrs 55 65 Payout/Settlement Physical, Par Versus Delivery, January 31, 2001

Suppose protection buyer buys 5 year CDS on reference obligation XYZ with coupon of 7.125 percent due 1/31/2010. The buyer pays the seller 65 basis points annually until trigger event happens. If no event the premium is lost in risk management. However, once event is happened, the protection seller is obligated to pay Par*(1-recovery value) of the reference debt as shown in the next slide.

Cash Flow of Five-Year Credit Default Swap

Party A Protection

Buyer

Party B Protection

Seller Receive face value of debt issued by Party C contingent

on trigger events

Pay annuity of [65 bps x $10 million]

Protection buyer in the above exhibit pays an annuity of $65,000 until the time the trigger events happens or up to 5 years with no event happening. Once trigger events happen, the protection seller is expected to pay the protection buyer $10 million*(1-recovery value of bond). Suppose after 3 months from the date of default recover rate is equal to 45 percent determined by polling agent for protection seller. The protection seller will be expected to pay the buyer $5.5 million.

Triggered Events

The credit event(s) that obligates the seller of the CDS to pay the buyer may include some or all of the followings:

- Bankruptcy -  Counterparty failure to pay -  Material restructuring debt - Capital control/moratorium - Obligation acceleration or default - Downgrade Receivership

Pricing CDS

The price of CDS can be estimated as a portfolio of long position at:

the frn at LIBOR + q bps plus a long position on the CDS on the same bond at the cost of z bps

to produce a synthetic default free frn as follows.Long frn+ long CDS=synthetic risk free frn Suppose the bid/offer spread is 1/8 on the LIBID/LIBOR, and TED

is 12.5 basis points resulting at a default swap spread of z as follows:

LIBOR + q – z = LIBID - TED LIBOR – LIBID = z-q- TED z = q +25 bps z = 175 bps

Probability of Default

Pdf = Pd + long put

Where Pdf and Pd are default-free and risky defaultable debt.

PD = [1- (Pd / Pdf )] (1- R)

PD = [1-(75.08/78.35)] (1- R) = .041

: Moody’s Average 1-year credit ratings transition matrix, 1920-1996.

Rating from:

Aaa Aa A Baa Ba B Caa-C Default WR

Aaa 88.32% 6.15% 0.99% 0.23% 0.02% 0.00% 0.00% 0.00% 4.29%

Aa 1.21% 86.76% 5.76% 0.66% 0.16% 0.02% 0.00% 0.06% 5.36%

A 0.07% 2.30% 86.09% 4.67% 0.63% 0.10% 0.02% 0.12% 5.99%

Baa 0.03% 0.24% 3.87% 82.52% 4.68% 0.61% 0.06% 0.28% 7.71%

Ba 0.01% 0.08% 0.39% 4.61% 79.03% 4.96% 0.41% 1.11% 9.39%

B 0.00% 0.04% 0.13% 0.60% 5.79% 76.33% 3.08% 3.49% 10.53%

Caa-C 0.00% 0.02% 0.04% 0.34% 1.26% 5.29% 71.87% 12.41% 8.78%

On the investment grade bonds up to Baa, the probability of migration (moving from a notch, say from A to Aa) is 2.3 percent, while probability of downgrade on the same issue from A to Baa is 4.67 percent as reported by Moody’s.

Average Recovery Rates on U.S. Corporate Bonds

Class Mean(%) Standard Deviation

Senior Secured 52.31 25.15

Senior Unsecured 48.84 25.01

Senior Subordinated 39.46 24.59

Subordinated 33.17 20.78

Junior Subordinated 19.69 13.85

Senior secured creditors on average is expected to recover; .52+/-.25 on every dollar, that is as high as 77 cents to low of 27 cents. Assuming distribution of credit loss is normal, 68 percent (+/- one standard deviation from the mean) of the creditors are expected to receive anywhere from 77 to 27 cents on a dollar in the bankruptcy court.

Argentina Sovereign Spread

Fixed-Rate Coupon Maturity Time to Maturity Bid Price Yield to Maturity U.S. Tsy Yield Spread

10.950% Nov. 99 1.03yr. 94.50 16.99% 4.03% 12.96

9.250 Feb. 01 2.34 96.00 11.23 4.08 7.15

8.375 Dec. 03 5.16 93.00 10.14 4.21 5.16

11.000 Oct. 06 7.97 96.50 11.69 4.51 7.97

Time to Expiration Sell Default Protection Buy Default Protection

3 years 9.00% 10.00%

5 8.00 9.00

10 7.50 8.00

Credit spread is not equal to the average price of credit default swap for Argentina sovereign debt. Theoretically, the average cost of default protection has to be equal to the spread of defaultable debt (Argentina bond) and default free instrument (the US bond). Deviation from parity is due to absence of liquidity of risky bond and other factors. For example, buying 9.25 percent Feb 01 Argentina sovereign bond that yields 11.23 percent and buying 3 years default protection (paying 10 percent), results 1.23 percent. On the other hand simply buying the US Treasury on the same time produces 4.08 percnet yield.

Synthetic structure

Pdf - Pd = long put (long CDS)

Example: Buying December 03 bond and buying protection produces return of (10.14 minus 9%). This return is 3.07 percent less than the return in a default free Treasury bond yielding 4.21%.

Sell February 01 and buy the U.S. treasury yielding 4.08 percent and selling 3-year default swap for 9 percent. This scenario produces total return from the synthetic long bond of 13.08 percent (4.08 percent plus 9 percent for selling CDS) as compared to the cash market yield of 11.23 percent picking up 185 basis points more in the synthetic structure.

Pd = Pdf - long put -long put = short put Investors can write default swap (sell protection), by posting

required margin and simultaneously buying risk-free instrument Pdf. The synthetic risky asset created usually has a higher yield than the yield on the cash market instrument.

Credit Default Swap Applications

Banks with credit exposure to corporate or sovereign bonds can be able to mitigate their risk through: Purchasing credit default protection Sell the loan in the secondary market

Banks who are willing to reduce concentration risk Sell default protection Buy a bond issued by an obligor to which they wish to have

exposure Lend money to an obligor to which they wish to have an

exposure Buy Credit-linked notes

Buyers of the default protections are:  Commercial Banks Non-financial corporations  Actively managed debt funds  Hedge fundsSellers of default protections are: Life insurance companies Reinsurance companies Major banks Collateralized debt obligations Commercial paper conduits

Credit Linked Notes

$1.1 billion 5-year Loan Five-year CLNs $1.1 billion proceeds Return of P&I Initial Loan

Citigroup

Trust

Enron

Investors

Citigroup having extended $1.1 billion loan to Enron, mitigated its exposure to Enron by creating a Trust who sold 5 year credit link note to investors. The 5 year note had slightly higher yield and investors were expected to continue receiving the coupon from the note as if it is the Citigroup obligations. However, in the event Enron defaulted, the investors to get only the recovery value of the Enron debt insulating Citigroup from such event. Citigroup therefore, securitized on balance sheet asset by creating an SPV(trust) who sold the risk to investors for some returns.

Fully Funded Securitization

Senior Notes

Loans proceeds 100 % Proceeds Sub-Notes

Proceeds

Bank SPV

Senior Notes

Subordinated Notes

Investors

Other Banks

A bank through CLO transaction can reduce its liabilities; improve on its higher rated lower yielding assets thereby increasing return on assets and return on equity.

Reduce concentration risk: CLO enables a bank to transfer its credit exposure to a particular borrower and a particular industry to the capital market fairly efficiently. The bank in the process of securitization assumes other credit risk to which it wishes to have greater exposure.

A bank can be able to manage its liquidity, credit spread, and concentration of assets tied to floating rate index such as LIBOR through its CLO transaction thereby improving asset/liability management.

Preserving bank-clientele relationship as the CLO enables the bank to sell its loan without damaging relationship with its customer, since the sponsor and the portfolio manager of the SPV trust is the affiliate of the bank and there is no need to notify the client in selling or assigning of the loans as is the case in selling loan in a whole loan basis.

Benefits of the structuring CLO

Synthetic CLO

Synthetic CLO emulates the cash CLO by transferring credit risk of the reference assets to the capital market through credit derivatives such as total return swap, credit default swap, or through issuing credit-linked notes without actually transferring the ownership of the assets to the bankruptcy-remote SPV trust.

Regulatory Capital relief Risk transfer Arbitrage profit Restructuring balance sheet

Motivations for structuring synthetic CLO/CBO

Synthetic Partially Funded CLO

Premium J.P. Morgan proceeds D

Bank loan Portfolio Senior

Tranche

Subordinated Tranche

SPV Trust Senior Notes Bankruptcy- remote assets Sub-Notes

Investors

Bank

Default protection

Premium

Default protection on sub-tranche

Proceeds

Sub-Notes

There are two, arbitrage and balance sheet. The arbitrage CLO, usually undertaken by

insurance companies, asset management, and investment banking firms to exploits yield miss-match (spread) on the underlying pool of assets and the lower cost of servicing CLO liabilities.

The balance sheet CLOs are employed by banks to mitigate and manage regulatory and risk-based capital.

Types of Synthetic CLO

The cash CLO on corporate exposure is 100 percent risk-weighted, while for synthetic CLOs, the risk-weighting is much less, reflecting the funded portion of the structure that is backed by government securities that is zero risk-weighted.

The above phenomena has prompted European banks to issue synthetic CLO by taking advantage of the fact that capital adequacy requirements (8 percent minimum capital on corporate exposure) do not differentiate between various levels of operating, market and credit risks.

Risk Weighting

The BIS capital requirements for various classes of debts for on-balance sheet requirements are as follows:

The sovereign government debt of the member of Organization of

Economic Cooperation and Development (OECD) is assigned zero BIS risk weight, these debts are treated as risk free and banks are not required to hold any reserve capital against them.

The senior debts of the banks from OECD are assigned 20 percent BIS risk weight; the banks are required to hold 1.6 percent (.20 x.08) of reserve capital for this type of debts. For example, a bank has to hold $320,000 in reserve capital (.20 x .08 x $200,000,000) for $200 million investment in a Mexican bank note.

Unfunded corporate revolving credits is assigned a 50 percent risk weight, the bank is required to hold a 4 percent (.50 x .08) reserve capital.

For all others, including corporate debts, funded revolving credit, non-OECD sovereign debts 100 percent BIS risk weight is assigned, requiring financial institutions to hold 8 percent reserve capital against the risk based assets.

BIS capital requirements

Total Return Swaps

TRS are HLT that motivate the receiver to take on the credit risk of an asset it does not own.

The bank who wishes to layoff the risk to the reference asset has high concentration risk.

The bank motivations may include: Reducing exposure without selling the asset Preserving banking relationship with the client Realizing regulatory capital relief Managing balance sheet to originate

Total Return Swap: Example

• A Bank enters into a TRS with a hedge fund on the reference credit rated BBB to layoff credit risk, with the notional principal of $50 million. The bank agrees to pay LIBOR+300bps+MV and receives LIBOR + 75 bps.

Bank

Buyer of protection

Hedge Fund

Seller of protection

LIBOR+300 bps+ MV

LIBOR + 75 bps

Motivations of the Receiver of TRS

The receiver is likely to have a host of reasons to enter into this HLT, for example:

Financing huge transaction with limited capital Exploiting the leverage as the return/risk can be

magnified Arbitrage profit albeit risky Access to capital market not previously available Sectoral arbitrage of credit risk in the high yield market

Total Return Swap Payoff to the Receiver Assuming 5 to 10 percent Collateral

Posted by Hedge Fund on Notional Principal of $50 Million

Bond price Capital Gain Coupon Interest Interest Return Return in one year Loss Net on 5 % on 10 % realized Realized +225 bps Collateral* Collateral* 5 % 10 % Collateral Collateral 103 1,500,000 1,125,000 125,000 250,000 110 % 60 % 100 0 1,125,000 125,000 250,000 50 27.50 97 -1,500,000 1,125,000 125,000 250,000 -10 -2.5 95 -2,500,000 1,125,000 125,000 250,000 -50 -22.50 92 -4,000,000 1,125,000 125,000 250,000 -110 -52.50

*Assuming 5 percent interest is earned.

Leverage Impact on Return on Regulatory Capital

100 % BIS 20 % BIS Notional $30 million $30 million Reserve .08 .08 Risk weight 100% 20 % Capital Required .08 x 100% x $30 M .08 x 20% x $30 M Spread earned 55 bps 55 bps Income $165,000 $165,000 Return on Capital 6.875% 34.375 %