*Coupled Lattice Efficiency Analysis (PATENTED)

CLEAN™* A Patented Approach to MBS Valuation

2

Heard It Through The Grapevine

"The actual sensitivity of MSRs to implied volatility is complex and somewhat controversial”Ben Golub in "Mark-to-Market Methodology, Mortgage

Servicing Rights, and Hedging Effectiveness“ “The model we use doesn’t even get the sign right

for volatility hedging of MSRs”A/L management advisor

“The price response to skew adjustment seems exaggerated”Hedge fund manager

Why do intuition and model disagree when it comes to

volatility?

3

Observations

Modeling prepayments is only a means to an end The goal is proper valuation and risk measurement

A mortgage is a callable amortizing bondPrepayment models should be consistent with callable bond models

Bonds (mortgages) are refunded (refinanced) when the call option is worth more dead than alive

Therefore bond and mortgage models should respond similarly to interest rate levels and volatility changes

4

Dynamic Versus Static Variables In an MBS model

Interest rate driven prepaymentsDynamically hedgedModeled using a stochastic interest rate process

Other prepayments, such as turnover and defaultsEither not hedged or statically hedgedModeled statically in CLEAN

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A financial engineer homeowner uses an option valuation model

Refinances optimally

Others refinance too early or too lateEarly refinancers are called “leapers”

Rarely occurs

Late refinancers are called “laggards”

AKA analysis shows that the 50 bps rule of thumb is sensible

Most homeowners refinance near-optimally!

Optimum Option Exercise Provides Benchmark for Suboptimal Behavior

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MBS Valuation Using CLEAN™

Two separate yield curves are requiredOne calibrated to mortgage ratesOther calibrated to MBS yieldsModeled using coupled lattice

Mortgage rates used to determine refisUsing notion of call efficiency

MBS rates used for discounting MBS cash flows

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Benchmark yield curve and volatilityUSD swap curve and appropriate swaption vol

Prepayment parameters Laggard distributionTurnover speed vectorDefault/buyout speed and recovery percentage vectors

Refinancing costFixed percentage of original principal

Homeowner credit spread Analogous to corporate credit spread

MBS price/OASFor EOD pricing, use OAS calibrated to TBA prices

CLEAN™ Model Input Parameters

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Calibration of CLEAN™: Straightforward and Intuitive

Rarely adjustedLaggard distributionTurnover speedDefault recovery percentageRefinancing cost

Occasionally adjustedHomeowner credit spreadDefault/buyout speed

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Calibrating Homeowner Credit SpreadFor Agency Pools

Should be consistent with prevailing mortgage ratesApproximately 120 bps for current coupon pools

Implies refi option premium of approximately 40 bps

Higher credit spread for higher coupon collateralImplies weaker credit, ceteris paribusCalibrated to dealer consensus duration/convexity, and specified pool

pay-up grids

Additional factors that can be incorporated:Fannie/Freddie vs. Ginnie/FHALTV, FICOYear of originationLoan sizePercent of non-owner occupied (low refi rate, high turnover rate)Average points paidCredit migration

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Estimated Homeowner Credit Spread FNMA TBA Coupon Stack – July 23, 2010

TBA  WAC (%)Homeowner Credit

Spread (bps)

FNCL 4 4.585 110

FNCL 4.5 4.950 110

FNCL 5 5.428 175

FNCL 5.5 5.949 240

FNCL 6 6.517 320

FNCL 6.5 6.975 400

FNCL 7 7.645 480

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OAS Implied by TBA Prices

FNMA 30-yr TBA OAS of CLEAN (July 23, 2010)

0

40

80

120

4.0 4.5 5.0 5.5 6.0 6.5

MBS coupon (%)

OA

S (

bp

)

10-yr agency spread

CLEAN

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CLEAN™ OAS Closely TracksAgency Debenture Spread

-50

0

50

100

150

1/1/2009 6/1/2009 10/30/2009 3/30/2010

Sp

rea

ds

(bp

s)

FNCL 4.5 OAS vs. Agency Debenture Spreads(1/2/2009 - 4/13/2010)

FNCL 4.5 OAS

10-yr agency spreads

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CLEAN™ OAS Movements Comparable to JPM OAS Movements

CLEAN vs. JPM FNCL 4.5 OAS (1/2/2009 - 7/19/2010)

-40

0

40

80

120

1/2/2009 7/3/2009 1/1/2010 7/2/2010

Sp

read

(b

ps)

CLEAN OAS (bp)

JPM OAS (bp)

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TBA Duration and Convexity: CLEAN™ vs. Other Models

7/23/2010

Turnover/default

rateHomeowner

credit spreadTBA

price

OAS

CLEAN JPMDealer model

BAML (new)

BAML (old)

FNCL 4 7% 110 101.84 23 8 25 1 -5

FNCL 4.5 9% 110 103.97 33 -2 34 -1 -11

FNCL 5 13% 175 106.19 53 -25 50 0 -33

FNCL 5.5 18% 240 107.72 67 -61 25 11 6

FNCL 6 24% 320 108.83 71 -71 29 16 24

FNCL 6.5 24% 400 109.81 97 -14 101 45 53Duration Convexity

CLEAN JPMDealer model

BAML (new)

BAML (old) CLEAN JPM

Dealer model

BAML (new)

BAML (old)

FNCL 4 4.9 5.0 5.2 4.5 4.5 -1.8 -2.0 -2.8 -3.0 -3.3

FNCL 4.5 3.5 2.9 4.2 2.6 2.8 -2.9 -3.4 -3.1 -3.9 -1.9

FNCL 5 2.7 1.3 3.7 1.4 1.8 -2.7 -2.9 -2.5 -2.8 0.2

FNCL 5.5 2.1 0.5 1.8 1.1 2.5 -2.2 -0.8 -1.4 -2.0 0.2

FNCL 6 1.9 0.5 1.3 0.6 2.5 -1.8 0.3 -0.9 -1.3 0.4

FNCL 6.5 2.3 1.4 2.9 0.5 2.5 -0.8 0.1 -0.4 -1.4 0.5

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TBA Price Movement vs. Model Implied Delta Movement

Actual Change in TBA Market Price vs. Sum of Implied Price Change Due to Risk Factors (1/2/2009 - 7/1/2010)

-3

-2

-1

0

1

2

3

1/1/2009 4/2/2009 7/2/2009 10/1/2009 12/31/2009 4/1/2010 7/1/2010% o

f p

ar

FNCL 4.5 Δ price

Σ implied price change due to risk factors

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Why CLEAN™ Is Ideal for Trading, Hedging, and Risk Management

Realistic transparent behaviorBased on well established financial and economic principlesInstead of mysterious mathematical formulas and parameters

Consistent with valuation models for callable bonds and cancelable swapsCalibration is straightforward and intuitiveConcretely defined model parameters

Easier to simulate

Model behavior always realisticBased on fundamental financial and economic principlesNot on statistical fitting of historical behavior

And ridiculously fastCriticial for simulation

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Modeling prepaymentsTurnover and defaults modeled using deterministic speedsRefinancings modeled using stochastic interest rate model

Modeling a mortgageAs a callable amortizing bondA financial engineer will refinance when the option is worth more dead than aliveOthers will refinance too early (never really happens) or too late (“laggards”)

Modeling heterogeneous refinancing behaviorDivide mortgage pool into 10 buckets according to laggard parameterUse a standard laggard distribution for a new pool

Modeling seasoned poolsFastest refinancing buckets disappear firstAutomatically accounts for ‘burnout’

The CLEAN™ Way

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References

Andrew Kalotay & Qi Fu (June 2009), A Financial Analysis of Consumer Mortgage Decisions, Mortgage Bankers Association.

Andrew Kalotay & Qi Fu (May 2008), Mortgage servicing rights and interest rate volatility, Mortgage Risk.

Andrew Kalotay, Deane Yang, & Frank Fabozzi (Vol. 1, 2008), Optimum refinancing: bringing professional discipline to household finance, Applied Financial Economics Letters.

Andrew Kalotay, Deane Yang, & Frank Fabozzi (Vol. 3, 2007), Refunding efficiency: a generalized approach, Applied Financial Economics Letters.

Andrew Kalotay, Deane Yang, & Frank Fabozzi (December 2004), An option-theoretic prepayment model for mortgages and mortgage-backed securities, International Journal of Theoretical and Applied Finance.

Available from http://www.kalotay.com/research