Option-adjusted 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 mortgage-backed 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.

Definition

In contrast to the simple "yield curve spread" measurement of bond premium over a pre-determined cash-flow 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 mortgage-payers will only tend to exercise this right when it is favourable for them and unfavourable for the bond-holder, buying an MBS partly involves selling an option. This is the source of the difference between the option adjusted spread (OAS) and the Z-spread (which ignores embedded options).

Since prepayments rise as interest rates fall and vice versa, the basic (pass-through) MBS has negative bond convexity (second derivative of price over yield). The MBS-holder's exposure to property-owner 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 OAS-figure 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

• Z-spread
• I-spread
• 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 Mortgage-Backed and Asset-Backed Securities. Wiley. ISBN 0-471-38587-5. 
• Hull, J. C. (2006). Options, Futures and Other Derivatives. Pearson. ISBN 0-13-149908-4. 

External links

• Miller, Tom (2007). Introduction to Option-Adjusted Spread Analysis. Bloomberg Press. ISBN 978-157660-241-6. 
• The Society of Actuaries review of the application of OAS to insurance, and other option adjustments. Society of Actuaries.