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14 The CFA Digest November 2003

2003, AIMR

DERIVATIVE INSTRUMENTS

The Complexities of Mortgage Options

Joseph R. PrendergastJournal of Fixed Incomevol. 12, no. 4 (March 2003):724

The author develops a framework to analyze the risk sensitivitiesof options on mortgage securities. He concludes that the con-vexity of a mortgage option is determined by the relationshipbetween the negative convexity of the underlying mortgageinstrument and the positive gamma of the mortgage option.

The author examines the risk sensitivities of mortgage options, which

are options written on mortgage forward agreements that have aspecified coupon and maturity date. The underlying instruments forthese forward agreements are pass-through securities insured by Fan-nie Mae, Freddie Mac, or Ginnie Mae. Mortgage options are tradedover the counter and are used to hedge the negative convexity inherentin mortgage instruments. Mortgage originators also use these optionsto reduce the risk of loans that have not yet closed.

The risk sensitivity of options is usually calculated with respect toprice changes in the underlying instrument. An options delta is theamount its price will change for a given change in the price of itsunderlying instrument, and an options gamma is the change in itsprice for a given change in its delta. The author suggests that usingyield as the variable to measure an options risk sensitivities providescomparable sensitivity measures to other fixed-interest instruments.Duration, for example, calculates the amount a fixed-income secu-

ritys price will change for a given change in interest rates, andconvexity measures the change in a securitys price for a given changein duration.

Joseph R. Prendergast is at Smith Breeden Associates . The summary was preparedby Richard D. Long, Jr., CFA, Principal Global Investors.

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The author considers an options convexity to be the result of theinteraction of the underlying instruments convexity and the options

gamma. This assumption implies that the convexity of a mortgageoption is determined by two factors: the negative convexity of theunderlying security and the positive gamma of the option. Becauseeither of these effects can dominate, the convexity of a mortgage calloption can be positive or negative. In this model, a mortgage putoption is always positively convex because the option is a shortposition on the negatively convex underlying security and the options

gamma is positive. For a call or put option on a security with zeroconvexity, the gamma of the option is the sole determinant of theoptions convexity.

The author believes that his findings will be useful for investors whoare reluctant to use mortgage options because they are unsure ofmortgage options effect on overall portfolio risk. To extend hisresearch, he suggests empirically investigating whether mortgage

options trade as implied in the model that he presents.Keywords: Derivative Instruments: debt derivatives; Debt Investments: asset-backed securities (including mortgage-backed securities)