- Option adjusted spread
**Option adjusted spread**(OAS) is the flat spread over the treasuryyield curve required todiscount a security payment to match its marketprice . This concept can be applied tomortgage-backed security (MBS), Options, Bonds and any other interest-rate Derivative.**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 ofvolatility :

*Variableinterest rate s

*Variableprepayment rates.Designing such models in the first place is complicated because prepayment variations are a

behavioural function of thestochastic 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. Sincemortgage -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 option adjusted spread (OAS).Since prepayments rise as

interest rate s fall and vice versa the basic (pass-through) MBS has negativebond convexity (second derivative of price overyield ). The MBS-holder's exposure to property-owner prepayment has several names:

*extension or contraction risk

*prepayment risk

*reinvestment risk (Lakhbir Hayre 's term)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.

**ee also***

Z-spread

*Convertible bond s 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*** [

*http://www.ordering1.us/bloombergbooks/product.php?sid=1&ccamp=RETAIL&pid=267 Introduction to Option-Adjusted Spread Analysis*] (ISBN 978-157660-241-6, Bloomberg Press, 2007)

* [*http://rmtf.soa.org/option_spread.pdf The Society of Actuaries review of the application of OAS to insurance, and other option adjustments*]

* [*http://www.belkcollege.uncc.edu/buttimer/MBAD%206160/Mortgage%20Backed%20Securities%20-%20Advanced%20Pricing%20and%20OAS%20Analysis.ppt OAS analysis using Monte Carlo with many power point examples*] (Deals with implying the OAS from the bond market prices. Estimate of minimum OAS = 150 basis points.)

*Wikimedia Foundation.
2010.*