Option pricing in a hidden Markov model of the short rate with application to risky debt evaluation

Abstract

Following the path initiated by Merton (1973), we study the option pricing problem in an economy with stochastic interest rates. We model the short rate dynamic by a diffusion process whose parameters are modulated by an underlying Markov process with jumps, as in Landen (2000). By exploiting the change of numeraire technique we obtain, under some assumption, a simple and easy to use call pricing formula which we then apply to the evaluation of risky debts so enlarging the flexibility of previous results obtained by Shimko et al. (1993). We also provide a detailed numerical study of call prices and credit spreads for a straightforward but interesting extension of the Vasicek dynamic included in our model.