# Option yield graph, About the Secretary

Definition[ edit ] In contrast to simpler "yield-curve spread" measurements of bond premium using a fixed cash-flow model I-spread or Z-spreadthe OAS quantifies the yield premium using a probabilistic model that incorporates two types of volatility : Variable interest rates Variable prepayment rates for an MBS.

Designing such models in the option yield graph place is complicated because prepayment rates are a path-dependent and behavioural function of the stochastic interest rate. They tend to go up as interest rates come down. Specially calibrated Monte Carlo techniques are generally used to simulate hundreds of yield-curve scenarios for the calculation.

Other definitions are rough analogs: Take the expected value mean NPV across the range of all possible rate scenarios when discounting each scenario's actual cash flows with the Treasury yield curve plus a spread, X. Treasury bonds or alternate benchmarks, such as the noncallable bonds of some other borrower, or interest rate swaps are generally not available with maturities exactly matching MBS cash flow payments, so interpolations are necessary to make the OAS calculation.

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Convexity[ edit ] For an MBS, the word "Option" in Option-adjusted spread relates primarily to the option yield graph of property owners, whose mortgages back the security, to prepay the mortgage amount. Since mortgage borrowers will tend to exercise this right when it is favourable for them and unfavourable for the bond-holder, buying an MBS implicitly involves selling an option.

The presence of interest-rate caps can create further optionality. The embedded "option cost" can be quantified by subtracting the OAS from the Z-spread which ignores optionality and volatility.

Since prepayments typically rise as interest rates fall and vice versa, the basic pass-through MBS typically has negative bond convexity second derivative of price over yieldmeaning that the price has more downside than upside as interest rates vary. The MBS-holder's exposure to borrower prepayment has several names: call risk.

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