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February 2010

Introduction to Bloomberg’s AOAS Pricing Modelfor Fannie Mae Callable Medium-Term Notes

SIFMA guidelines were introduced for pricing and trading European(one-time call) callable U.S. agency debt securities in 2003. Fannie Maebelieves this development further enhanced the transparency and liquid-

ity of large size, European-style callable medium-term notes (MTNs) inboth the primary and secondary markets. Bloomberg’s AOAS screenenables investors to value qualifying callable MTNs relative to a real-timeFannie Mae constant maturity yield curve derived from a live noncallableBenchmark Securities yield curve.

The guidelines recommend the use of a “single credit issuer specic”constant maturity curve, and the relevant swaption volatility to price thecallable bond on an OAS basis. For example, in analyzing qualifyingFannie Mae callable MTNs, Fannie Mae’s Benchmark Securities constantmaturity yield curve should be used. The guidelines are limited to callablesecurities that have European-style (one-time) calls and are callable atpar only on the call date, which must be a coupon date.

The security’s CUSIP is used to bring the security into AOAS for analysisby typing the Fannie Mae CUSIP number <CORP> AOAS <GO>. At anytime, any outstanding Fannie Mae callable debt security, with a European-style call, may be analyzed using the SIFMA guidelines. To perform analy-sis on these securities, investors have the option to change several of the variables while in the AOAS screen, including the yield curve, at-the-money volatility, OAS, price, and settlement date. Only the skew-adjustedvolatility and the forward strike rate may not be overridden. Additionally,AOAS requires that the investor enter either an OAS or price to solve for the other variable.

The AOAS pricing model for

qualifying Fannie Mae callable

medium-term notes (MTNs) using

a 4-year noncall 1-year European-

style callable MTN as an example.

The picture to the right is the AOAS

screen as it appears on Bloomberg

using an example of a Fannie Mae

4-year noncall 1-year European-

style callable MTN. The variables

are:

The noncallable Benchmark

Securities yield curve and

associated constant maturity yield

adjustment spreads are Fannie

Mae Benchmark Securities yield

curve provided by Bloomberg

Agency Composite (AGPX);

The corresponding mid-market,

at-the-money, European swaption

volatility;

Skew adjusted volatility;

Forward strike rate;

Settlement date;

Option Adjusted Spread (OAS),

and;

Dollar price

Users may substitute other values

for variables a, b, e, f, and g as

they deem appropriate. Thedefault and input variables are

explained in greater detail in the

pages that follow.

acbdfg

e

a

b

c

d

f

e

g

© 2010, Fannie Mae.



a

AOAS default variables

using 4-year noncall

1-year in the example:

Fannie Mae Noncallable

Benchmark Securities

Yield Curve.

2

Noncallable Benchmark Securities Yield Curve

Description of “Yield” column from a For large size, European-style callable MTNs, thedefault a constant maturity yield curve variable inAOAS is Fannie Mae’s Benchmark Securities con-stant maturity yield curve. The maturities deningthe curve include 3- and 6-months, 1-year, 2-, 3-, 4-,5-, 7-, 10-, 20-, and 30-years. The entire BenchmarkSecurities yield curve, except for the 20-year matu-rity yield, is fed to Bloomberg’s AOAS and updatedcontinually via data provided by broker-dealers. In thecase of the 20-year maturity yield, Bloomberg usesa straight-line extrapolation between 10-year and

30-year bullet Benchmark yields. The current 30-year on-the-run Benchmark Bond matures in November 2030. Because this 30-year bond has an effectivematurity of approximately 20-years, Bloomberg mustextrapolate between the 20-year and 30-year bul-let Benchmark yields. For 4- and 7-year maturities,Fannie Mae selects securities that have rolled downthe curve but are the most liquid issues. For all other maturities, securities are the on-the-run issues.

The yields provided for the AOAS application are themid-market yields (the average between the bid- andask-yields). The underlying securities that make upthe constant maturity yield curve may be viewed inBloomberg by typing AGPX <GO>.

Description of “Adjust” column from a

The column labeled “Adjust” is used to show the con-stant maturity adjustment spreads. For all the denedmaturity points, the adjustment spread is calculatedby subtracting the actual yield from a calculated con-

stant maturity yield for the same maturity point. Theseadjustment spreads are fed to Bloomberg’s AOAS andupdated on a real-time basis via data provided by bro-ker-dealers. The constant maturity calculation used inthe AOAS screen was developed by the SIFMA.

Investors can also use the AOAS screen to evaluatequalifying Fannie Mae callable MTNs with the swapscurve or the Treasury curve by substituting thesecurves for the Benchmark Securities default yieldcurve.



AOAS default variables

using 4-year noncall

1-year in the example:

Mid-Market at-the-

money European

swaptions volatility

The SIFMA model

default variables using

4-year noncall 1-year

in the example: Skew

Adjusted Volatility

b

c

3

At-the-money VolatilityThe default b volatility variable is the mid-market,at-the-money swaption volatility for a comparableEuropean-style option as quoted by the inter-dealer brokerage rm Tullett Prebon. The Tullett Prebonswaption volatilities are found in Bloomberg by typ-ing TTSV <GO> 1 <GO> 2 <GO>, for United StatesDollar Swaption Volatilities or on Reuter’s iCap —page 19902. The Tullett Prebon swaption volatilitiesare updated on a real-time basis and fed directly intoBloomberg. Investors may override the default volatil-ity assumption that appears in AOAS by changing it to

any desired value.The appropriate swaption volatility for the 4-year noncall 1-year callable MTN is the 1 into 3-year mid-market European swaption volatility. In the eventthat an exact match cannot be made to the matrixof swaption structures provided by Tullett Prebon, abilinear interpolation calculation will be used amongswaption structures most closely matching the FannieMae callable MTN.

Skew Adjusted VolatilityThe at-the-money (ATM) volatility variable c is ad-

justed for skew resulting in a skew adjusted volatilitythat more accurately reects current market condi-tions. The Black’s pricing framework assumes that theimplied volatility of an underlying asset is constant for different strike rates.

However, in-the-money (ITM) and out-of-the-money(OTM) options trade at different implied volatilitylevels than at-the-money options. Hence, volatilityskew is the difference in the implied volatilities of ATMand ITM/OTM options. The skew adjusted volatility

gure that is displayed in the AOAS screen cannotbe overridden as it is a calculated eld. However, theskew variable may be changed manually but is de-faulted, per SIFMA guidelines, to 1.00. Any change inthe skew variable (from 1.00) will result in a differentcalculated skew adjusted volatility.



4

The d forward strike rate variable shown in AOAS isimplied from the noncallable Benchmark Securities

yield curve, which is OAS adjusted. The forward yieldis implied by the current yield curve for the periodbeginning on the exercise date and ending on the ma-turity date of the underlying swap. This forward strikerate variable cannot be overridden.

AOAS default variable

using 4-year noncall 1-year

in the example: Forward

Strike Rate

The SIFMA model default

variables using 4-year

noncall 1-year in the

example: Settlement Date

d

e

The e settlement date variable for a new issuedefaults to the appropriate date at the announce-

ment of each issue. For a new issue, Fannie Mae willinput the settlement date. For outstanding issues or reopenings, the default settlement date in Bloombergwill need to be veried by the investor. Investors mayoverride the settlement date variable. However, themaximum settlement period for a trade that is beingpriced using the SIFMA guidelines is three businessdays.



5

OAS and Dollar Price

The f OAS of the callable MTNs will be priced onan OAS basis relative to the noncallable Fannie MaeBenchmark Securities yield curve. An investor caninput an OAS at which a specic transaction is beingmarketed or an OAS at which an investor is interestedin buying or selling a qualifying callable MTN to getthe corresponding dollar price.

AOAS investor input

variables using the

example of a new issue

4-year noncall 1-year:

(top) OAS and (bottom)

Dollar Price

f

c

g

© 2010, Fannie Mae.

No Offer or Solicitation Regarding Securities. This document is for general information purposes only. No part of this document may be duplicated, reproduced, distributed or displayed in public inany manner or by any means without the written permission of Fannie Mae. The document is neither an offer to sell nor a solicitation of an offer to buy any Fannie Mae security mentioned herein or anyother Fannie Mae security. Fannie Mae securities are offered only in jurisdictions where permissible by offering documents available through qualied securities dealers or banks.

No Warranties; Opinions Subject to Change; Not Advice. This document is based upon information and assumptions (including nancial, statistical, or historical data and computations based uponsuch data) that we consider reliable and reasonable, but we do not represent that such information and assumptions are accurate or complete, or appropriate or useful in any particular context, includingthe context of any investment decision, and it should not be relied upon as such. Opinions and estimates expressed herein constitute Fannie Mae’s present judgment and are subject to change withoutnotice. They should not be construed as either projections or predictions of value, performance, or results, nor as legal, tax, nancial, or accounting advice. No representation is made that any strategy,performance, or result illustrated herein can or will be achieved or duplicated. The effect of factors other than those assumed, including factors not mentioned, considered or foreseen, by themselvesor in conjunction with other factors, could produce dramatically different performance or results. We do not undertake to update any information, data or computations contained in this document, or to communicate any change in the opinions, limits, requirements and estimates expressed herein. Investors considering purchasing a Fannie Mae security should consult their own nancial and legaladvisors for information about such security, the risks and investment considerations arising from an investment in such security, the appropriate tools to analyze such investment, and the suitability of such investment in each investor’s particular circumstances.

Fannie Mae securities, together with interest thereon, are not guaranteed by the United States and do not constitute a debt or obligation of the United States or of any agency or instrumentality thereof other than Fannie Mae.

Conversely, the g dollar price at which an investor isinterested in analyzing or transacting a callable MTNmay be entered to obtain the corresponding OAS. Theassumption for the above calculation is that the volatil-ity being used has been set to a desired value, but thedefault volatility is the European swaption volatility.

It is also possible for the user to calculate an impliedc volatility using the AOAS screen for a given g price and f OAS level.

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