Since its inception in the 1970s, the mortgage-backed security market has experienced dramatic growth in the United States. As of June 30, 2002, the total notional amount of Agency mortgage-backed securities and collateralized mortgage obligations outstanding was more than $3.9 trillion. This means that the size of these markets now exceeds the $3.5 trillion notional amount of publicly-traded U.S. Treasury debt.

Despite the importance of these markets, however, the goal of developing a fundamental theory of mortgage valuation represents an ongoing challenge to researchers. The key element that has proven difficult to explain within a rational model is how mortgage borrowers choose to refinance their loans. Influential early work by Dunn and McConnell (1981a, b), Brennan and Schwartz (1985), and others applies contingent claims techniques to the problem by modeling prepayment as an endogenous decision made by the borrower in minimizing the present value of his current mortgage.

More recently, Dunn and Spatt (1986) and Stanton and Wallace (1998) extend this classical approach in an important way by modeling the prepayment decision as the result of the borrower minimizing his lifetime mortgage costs. As discussed by Schwartz and Torous (1989, 1992, 1993), however, actual prepayment behavior appears very suboptimal relative to the optimal behavior implied by these models. Furthermore, these models all have the property that mortgage-backed security prices cannot exceed par plus the number of points paid to refinance the loan. As demonstrated by Stanton (1995), Boudoukh, Whitelaw, Richardson, and Stanton (1997), and others, this upper bound is nearly always violated in practice.

A common feature throughout the earlier literature is the assumption that the rate at which a borrower can refinance his loan is independent of his financial status. In actuality, however, a borrower who does not satisfy the strictest underwriting guidelines may have to refinance at a higher rate than other more-qualified borrowers. This clearly would reduce his incentives for prepaying his current mortgage and affect his optimal refinancing strategy. Thus, even though principal and interest on an Agency mortgage-backed security are guaranteed, the actual timing of these cash flows could be affected by the credit of the borrower, which in turn would be reflected in the value of the security.

In this paper, we study the valuation of mortgage-backed securities when the borrower may only be able to refinance at a premium rate over the par mortgage rate because of his credit. Following Dunn and Spatt (1986) and Stanton and Wallace (1996), we solve for the optimal refinancing strategy of a borrower whose objective is to minimize his lifetime mortgage costs. Our approach also takes into account the effects of mortgage refinancing transaction costs and the probability of prepaying for exogeneous reasons. Since the nature of problem requires considering the effects of decisions going far beyond the current mortgage, it is important to use a modeling framework that reflects the actual intertemporal behavior of the term structure.

In light of this, we develop the model within a realistic multi-factor term-structure setting that matches both the current term structure and the values of fixed income options. The use of a multi-factor model is also consistent with Boudoukh, Whitelaw, Richardson, and Stanton (1997) and Downing, Stanton, and Wallace (2002) who find evidence that mortgage-backed security prices are driven by multiple term-structure factors. Since the recursive refinancing problem is essentially an American option valuation problem, we use the least-squares simulation method of Longstaff and Schwartz (2001) to solve for the optimal recursive strategy and value mortgage-backed securities in this multi-factor framework.

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