 Optionadjusted spread

Option adjusted spread (OAS) is the flat spread which has to be added to the treasury yield curve in a pricing model (that accounts for embedded options) to discount a security payment to match its market price. OAS is hence model dependent. This concept can be applied to a mortgagebacked security (MBS), option, bond and any other interest rate derivative. In the context of an MBS, the option relates to the right of property owners, whose mortgages back the MBS, to prepay the full mortgage amount.
Contents
Definition
In contrast to the simple "yield curve spread" measurement of bond premium over a predetermined cashflow model, the OAS describes the market premium over a model including two types of volatility:
 Variable interest rates
 Variable prepayment rates.
Designing such models in the first place is complicated because prepayment variations are a behavioural function of the stochastic interest rate. (They tend to go up as interest rates come down.)
OAS is an emerging term with fluid use across MBS finance. The definition here is based on Lakhbir Hayre's Mortgage Backed Securities text book. 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. The OAS is defined as the value of X equating the market price of the MBS to its value in this theoretical framework.
Treasury bonds may not be available with maturities exactly matching likely cash flow payments so some interpolation may be necessary to make this calculation.
Convexity
The word 'Option' in Option adjusted spread relates to the right of property owners, whose mortgages back the MBS, to prepay the full mortgage amount. Since mortgagepayers will only tend to exercise this right when it is favourable for them and unfavourable for the bondholder, buying an MBS partly involves selling an option. This is the source of the difference between the option adjusted spread (OAS) and the Zspread (which ignores embedded options).
Since prepayments rise as interest rates fall and vice versa, the basic (passthrough) MBS has negative bond convexity (second derivative of price over yield). The MBSholder's exposure to propertyowner prepayment has several names:
 extension or contraction risk
 prepayment risk
 reinvestment risk
This difference in convexity can also be used to explain the price differential from an MBS to a treasury bond. However, the OASfigure is typically preferred. The discussion of the "negative convexity" and "option adjusted spread" on a bond is essentially a discussion of a single MBS feature (prepayment risk) measured in different ways.
See also
 Zspread
 Ispread
 Convertible bonds must pay a similar increased yield (over the standard corporate bond) when they are callable by the issuing company.
 Monte Carlo techniques are used to derive the Option adjusted spread.
References
 Hayre, L. (2001). Salomon Smith Barney Guide to MortgageBacked and AssetBacked Securities. Wiley. ISBN 0471385875.
 Hull, J. C. (2006). Options, Futures and Other Derivatives. Pearson. ISBN 0131499084.
External links
 Miller, Tom (2007). Introduction to OptionAdjusted Spread Analysis. Bloomberg Press. ISBN 9781576602416.
 The Society of Actuaries review of the application of OAS to insurance, and other option adjustments. Society of Actuaries.
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