The Effect of Alternative Interest Rate Processes on the Value of Mortgage-Backed Securities

Analytical valuation of mortgage-backed securities (MBS) requires a process for generating future interest rates to value the embedded prepayment option. While many single-factor interest rate models are available, no systematic comparison of their effects on MBS values has been published. This article compares valuation results using three such processes—a simple log-normal process; the square-root process of Cox, Ingersoll, and Ross (CIR); and the no-arbitrage process of Black, Derman, and Toy (BDT)—selected for their prominence in the literature and their differences in major characteristics. The study compares how well the models fit actual Treasury yield curves and their valuation of simulated MBS. The simple log-normal process is rejected for its inconsistent performance in fitting yield curves. The CIR and BDT processes value noncallable mortgagelike cash flows similarly, but the CIR process values the call option more and so has lower callable values for the MBS.