Pricing mortgage-backed securities using prepayment functions and pathwise Monte Carlo simulation.

by Acheampong, Osman K.

To value any fixed income security one needs to evaluate the discounted expected cash flows according to an arbitrage free interest rate model. In the case of mortgage-backed securities the future cash flows are uncertain due to mortgagors exercise of their prepayment options. The present project considers prepayments which result from interest rate dependent complete refinancing of mortgages in a pool. The rate of refinancing is modeled as an arbitrary, user defined function of current and past interest rates. This enables the inclusion of refinancing rates that depend on not only on the current level of interest rates but also on the trend of the interest rates and that may also exhibit burnout effects due to past periods of low interest rates. The resulting cash flows depend on the entire past of the path that the interest rates took to get to the current level. The Black-Derman-Toy arbitrage free binomial tree is used to model the underlying interest rates. This is a single-factor market price consistent model which also allows the specification of the observed volatilities. Monte Carlo methodology is used to simulate random paths in the interest rate tree to evaluate the cash flows along the path. A computer program written in MAPLE implements the entire process. 4