Pricing of Interest Rate Sensitive Instruments Under Markovian Interest Rate Models
18 Pages Posted: 2 Jan 2007
Date Written: June 2006
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.
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