Pricing Bonds and Bond Options with Default Risk

Abstract

The pricing of bonds and bond options with default risk is analyzed in the general equilibrium model of Cox, Ingersoll, and Ross (Cir, 1985). This model is extended by means of an additional parameter in order to deal with financial and credit risk simultaneously. The estimation of such a parameter, which can be considered as the market equivalent of an agencies' bond rating, allows to extract from current quotes the market perceptions of firm's credit risk. The general pricing model for defaultable zero-coupon bond is derived in a simple discrete-time setting while a more rigorous treatment, in a continuous-time setting, is contained in the Appendix A. Defaultable bonds may be valued by discounting the promised terminal payoff at a default-risk-adjusted interest rate, i.e. the risk-free rate plus a default-risk premium, or by discounting the expected terminal payoff at a risk-free interest rate. The availability of an integrated model allows for the pricing of default-free options written on defaultable bonds and of vulnerable options written either on default-free bonds or defaultable bonds. Valuation is performed under different contractual provisions dealing with the event of default: their impact on options prices is investigated and several numerical examples are given. A comparison between our results and those given by Jarrow and Turnbull (1995) is also presented.