Pricing of Interest Rate Sensitive Instruments Under Markovian Interest Rate Models

Abstract

Markovian interest rate models are very popular for the pricing and hedging of interest rate sensitive products. In this paper we implement interest rate models that depend on a finite Markov chain. We construct the primitive Arrow-Debreu security prices and show how bonds, bond options and other interest rate sensitive instruments such as caps and swaptions can be priced. By introducing a carefully selected 'pilot process' we can reduce the dimensionality of the parameter set, while maintaining a sufficient degree of flexibility. We also show how the Markov chain model can be used to approximate virtually any jump-diffusion interest rate specification. Examples based on the popular CIR interest rate model illustrate the implementation of this approach and highlight its potential to be accurately calibrated to market instruments.