Valuation of Mortgage-Backed Securities Based upon a Structural Approach

This paper studies the valuation of mortgage-backed securities (MBS) based upon a structural approach of several risks involving the prepayment and/or default behavior of mortgagors. For the Kariya and Kobayashi (1999) model using a time-consuming Monte-Carlosimulation, we provide an alternative semi-analytic valuation methodology closely related to solving the (Volterra type) integral equation with respectto the first hitting time density for a curved/flat boundary; consequently that enables us to calculate the MBS price faster and more precisely. Next, to capture the path-dependent prepayment behavior of the interest ratemovements we give some prepayment models based upon a two-dimensional Markov process of the interest rate and its long-run average rate. Third, we study the simultaneous assessment issue of prepayment and defaultrisks, encountered in practice.Finally we discuss the calculation of the joint probability density ofmultiple first hitting times.