An Arbitrage-Free Estimate of Prepayment Option Prices in Fixed-Rate Gnma Mortgage-Backed Securities

Abstract

In an efficient market, the no-arbitrage condition implies that the price difference between two assets is the market value of all differences in their cash flows. We use this logic to deduce the price of the prepayment option in fixed-rate GNMA mortgage-backed securities. The option price 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 replicates the promised GNMA cash flow, assuming prepayment is precluded. We find that five key regressors explain more than 90% of the prepayment option value in pooled time-series cross-sectional analysis. Also, the time values of the prepayment option calculated display a pattern similar to the Black-Scholes (1973) option pricing method. Another result is the existence of negative option prices and the negative time value of the option prices. Our method is independent of assumptions regarding interest rate processes and the homeowner's prepayment behavior, and it provides a benchmark for testing theoretical prepayment models.

JEL Classification: E4, G21