VALUATION OF CMOS

VALUATION OF CMOS

IntroductionSTATIC VALUATIONDYNAMIC VALUATION MODELINGOption-adjusted spread(OAS) Other products of the OAS modelsIllustration Plain vanilla structure A PAC/Supports structure A reverse pay structure

STATIC VALUATION

Average life

Static Spread refinancing rate fixed Zero volatility OAS

received principal Total

T at time Principal T1 at time Principal 1

DYNAMIC VALUATION MODELING

Option-adjusted spread(OAS)A measure of the yield spread that can be

used to reconcile dollar differences between value and price

using simulation to generate Monthly cash flows are path-dependent

SIMULATIONStep 1 : generating many scenarios of

future interest rate path

SIMULATIONStep 2 : generating refinancing rate

corresponding to the scenarios

SIMULATIONStep 3: generating cash flow

SIMULATIONStep 4 : generating spot rate

1 11 1 nZ /121T T

T nfnfnf

SIMULATION

T

T

TT

KnZ1

nCnCPV

N

NPath PV 2Path PV 1Path PV PriceMarket

nC PVnC PVnC PV nPath PV 36021

INTERPRETATION OF OAS

Be used to reconcile value with market price

Be measuring the average spread over the Treasury spot rate cure， not the Treasury yield curve

An average spread

Option cost = Static spread – Option-adjusted

spread

OPTION-ADJUSTED DURATION

Measure the price sensitivity of a bond to a small change in interest rates.

Duration= P- - P+ / P0 (y+ -y-) Effective durationAssume: parallel shift in the yield curve

 

  Increase in price Decrease in price

Positive convexity X% Less than X%

Negative convexity X% More than X%

OPTION-ADJUSTED CONVEXITY

•Convexity is the rate of change of the dollar duration of a security•When the prevailing mortgage rate is much higher than the mortgage rate ---Positive convexity •Effective convexity

Simulated Average Life

Is the average of the average lives along the interest rate paths

The greater the range and standard deviation of the average life, the more the uncertainty about the tranche’s average life

structure

Plain Vanilla Structure

Base case (assumes 12% interest rate volatility)C is better--- high OAS but low option cost

PrepaymentSlow--- OAS decrease, IO increase

VolatilityIncrease---longer tranches benefit more

PAC/Support Bond StructureStructure

Base case

prepayment

volatility

Reverse PAC Deal

structure

After support goes,can move prepayments down to last tranche, protect higher classes from contract risk

  Average Life

OA-Duration

OA-Convexity

PAC C 10.9 6.3 -0.22

PAC D 19.7 5.9 0.04

THE END