Binomial pricing of fixed-income securities for increasing and decreasing interest rate cases

摘要

The option features embedded in many bonds and fixed-income securities have made the binomial interest rate tree approach to bond valuation a valuable model for pricing debt securities. Fundamental to the application of the binomial model to bond valuation is the assumption about the underlying stochastic process. There are two general approaches to modelling stochastic interest rate movements using a binomial model - the equilibrium model and the calibration model. Both models assume that the interest rate's logarithmic return is normally distributed. However, a number of empirical studies have provided evidence that the return distributions of a number of securities exhibit persistent skewness. In modelling interest rate patterns, the existence of skewness in a binomial process impacts not only the values of the up and down parameters, but also the probabilities of the underlying rate increasing or decreasing each period. The purpose of this study is to show how a binomial model of interest rates can be extended to incorporate skewness and to illustrate the impact skewness can have on the pricing of bonds and mortgage backed securities - a security whose discount rate, as well as cash flows, are sensitive to interest-rate risk.