Derivative mortgage-backed securities from fixed-rate and adjustable-rate mortgages: Empirically derived prepayments and valuation

This study examines two valuation methods for derivative mortgage-backed securities. The first method uses a two factor model of interest rates with an empirically obtained prepayment function, where prepayments are modeled as an additional component of cash flow in the bond valuation equation. Monte Carlo simulation is used for solving the equation. The second method uses the Refinancing Threshold Pricing model with the one factor model of interest rates, where prepayment is modeled as a boundary condition. Heterogeneity of mortgagors in a pool, across planned termination dates and refinancing costs, is assumed. The use of scenario analysis as a means for hedging against interest rate risk is then discussed. This study also consists of an empirical analysis of two different models for estimating prepayments, in a dynamic environment, on Adjustable-Rate Mortgages (ARMs), and their subsequent use for the valuation of mortgage-backed securities. The first prepayment model is a proportional hazards model, which is estimated using the method of partial likelihood. The second model uses logit to estimated prepayments on ARM pools. The values of the securitized form of ARMs are then determined using contingent claims analysis, treating these securities as essentially default-free. The Brennan and Schwartz two factor model is used to estimate the yield curve, and Monte Carlo simulation is employed to solve the differential equation governing the values of these securities. The values of ARMs under different sets of contractual features, viz., periodic and life-of-loan caps and margins on the index, are studied