Pricing a Defaultable Convertible Bond by Simulation

Abstract

In this study, we offer a simple way to price a defaultable, convertible, and callable bond by applying the Longstaff-Schwartz Least Squares simulation method. In our model, the stock price is a driving force for valuing the security. A key idea is to terminate the simulated sample path immediately when the issuer defaults on the bond at time t, the same as when the investor and the issuer optimally exercise their option, and to discount back the resulting cash flows at a risk-free rate. In turn, the defaulted group of the sample paths belongs to a bottom x percentile of the realized stock prices at each time, which is exogenously given by the cumulative or marginal default probability of a firm equally rated as the issuer. We apply our simulation model to a zero-coupon, callable, convertible and defaultable bond and show that the price depends on its default probability and recovery ratio.