Pricing Fixed-Income Derivatives Under Increasing and Decreasing Interest Rate Cases Using a Skewness-Adjusted Binomial Interest Rate Tree

There are two general approaches to modeling 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 modeling 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. In this paper, we present empirical evidence showing the significance of skewness when interest rates are increasing and decreasing. We next illustrate how the Johnson, Pawlukiewicz, and Mehta skewness-adjusted binomial model can be used to calibrate a binomial interest rate tree for increasing and decreasing interest rate cases in which the end-of-the period distribution is characterized by skewness. Using the skewness-adjusted binomial equilibrium model, we then compare the prices of option-free bonds and bond derivatives under stable, increasing, and decreasing rate scenarios