AN ARBITRAGE-FREE ESTIMATE OF PREPAYMENT OPTION PRICES IN FIXED-RATE GNMA MORTGAGE-BACKED SECURITIES

In an efficient market, the no-arbitrage condition implies that the pr ice difference between any two assets must be the market value of ail differences in their cash flows. We use this logic to deduce the price of the prepayment option embedded in fixed-rate Government National M ortgage Association (GNMA) mortgage-backed securities. The option pric e equals the difference between an observed GNMA price and the cost of a synthetic, nonprepayable GNMA constructed from the least expensive portfolio of Treasury securities that exactly replicates the promised GNMA cash flow stream, assuming prepayment is precluded. We regress th e option prices on variables found significant in previous prepayment studies, finding that five key regressors explain more than 90% of the prepayment option value in pooled time-series cross-sectional analysi s. We also show that the time value of the prepayment option calculate d by our method displays a pattern similar to that produced by the Bla ck-Scholes (1973) option pricing model. An additional empirical result is the existence of negative option prices and negative time value of the option prices. We attribute these to the fact that homeowners som etimes exercise their prepayment options when they are out-of-the-mone y, and to refinancing transaction costs. Our method is independent of assumptions regarding interest rate processes and the homeowner's prep ayment behavior, and it provides a benchmark for testing theoretical p repayment models.