Option-adjusted spread

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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 primarily to the right of property owners, whose mortgages back the MBS, to prepay the mortgage amount.


In contrast to the simple "yield curve spread" or "Z-spread" measurement of bond premium over a fixed cash-flow model, the OAS describes the market premium over a model including two types of volatility:

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 textbook. 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.


The word 'Option' in Option-adjusted spread relates primarily to the right of property owners, whose mortgages back the MBS, to prepay the mortgage amount. Since mortgage-payers will 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. (The presence of interest-rate caps can create further optionality.) This is the source of the difference between the option-adjusted spread (OAS) and the Z-spread (which ignores optionality and interest-rate 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 yield). The MBS-holder's exposure to property-owner prepayment has several names:

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" of a bond is essentially a discussion of a single MBS feature (rate-dependent cash flows) measured in different ways.

See also[edit]

  • 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.


  • 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[edit]