VALUATION OF CMOS

Introduction STATIC VALUATION DYNAMIC VALUATION MODELING Option-adjusted spread(OAS) Other products of the OAS models Illustration Plain vanilla structure A PAC/Supports structure A reverse pay structure

STATIC VALUATION Average life Static Spread  refinancing rate fixed  Zero volatility OAS

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

SIMULATION Step 1 : generating many scenarios of future interest rate path

SIMULATION Step 2 : generating refinancing rate corresponding to the scenarios

SIMULATION Step 3: generating cash flow

SIMULATION Step 4 : generating spot rate

SIMULATION

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 + / P 0 (y + -y - ) Effective duration Assume: parallel shift in the yield curve

Increase in priceDecrease in price Positive convexityX%Less than X% Negative convexityX%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

Prepayment Slow--- OAS decrease, IO increase

Volatility Increase---longer tranches benefit more

PAC/Support Bond Structure Structure

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 PAC D

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