The Term Structure of Interest Rates in a Markov Setting

R.J. Elliott and C.A. Wilson (Canada)


Interest Rate Modeling, Term Structure, Derivatives,Markov Chain


An interest rate model is described in which randomness in the short-term interest rate is due entirely to a Markov chain. We model randomness through the mean-reverting level rather than through the interest rate directly. The short-term interest rate is modeled in a risk-neutral setting as a continuous process in continuous time. This allows the valuation of interest rate derivatives using the martingale approach. In particular, a solution is found for the value of a zero-coupon bond. We also show how to incorporate the initial term structure to calibrate the model for arbitrage free bond prices. The model is shown to encapsulate sev eral empirically observed features associated with interest rate time series.

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