The Valuation of Options on Bonds with Default Risk

In this paper we present a model for valuing European and American options, which incorporates both default and interest rate risks. We develop a framework that permits evaluation of three kinds of options: (i) options issued by default-free counterparties on risky bonds, (ii) options issued by risky counterparties on default-free bonds and (iii) options issued by risky counterparties on risky bonds — a case where default risk enters at both levels. We show that the price of a put option on a risky discount bond is hump shaped for a European put and monotone increasing for an American put. We also find that the price impact of default risk is less for an American put option than for a European one.