A model for the valuation of adjustable-rate mortgage-backed securities with the two-factor HJM term structure model

An investment into an ARM-backed security requires the estimation of its theoretical, "fair", value, which can be determined using a stochastic valuation model and a well-specified prepayment function. In this study, we develop a general framework for the valuation of ARM-backed securities, based on the two-factor Heath, Jarrow and Morton (HJM) (1992) term structure model and non-linear prepayment functions. The HJM specification is well suited for the valuation of ARM-backed securities, for it allows to explicitly model both short-term and long-term interest rates. Prepayment function is estimated by the Cox proportional hazards model and the spline technique. We further demonstrate how the price of an ARM-backed security is affected by the choice of the prepayment model. ARM-backed securities are then priced by the method of Monte Carlo simulation. We find that the Cox proportional hazards model outperforms the spline technique. The investment value of a convertible ARM-backed security is also influenced by the short position that an investor takes in the embedded conversion option. To value the conversion option, we estimate a prepayment function for convertible mortgage pools. The theoretical value of the conversion option is calculated as the difference in model prices of non-convertible and convertible ARM-backed securities. We further investigate the sensitivity of the conversion option value to ARM contractual features and the interest rate related factors. We show that the conversion option reduces the value of an ARM-backed security to an investor because convertible loans exhibit prepayment rates which are faster and more sensitive to the interest rate fluctuations than those for non-convertible loans.