THE TERM STRUCTURE OF INTEREST RATES IN A MARKOV SETTING

摘要

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 several empirically observed features associated with interest rate time series.