Abstract

Pricing of Defaultable Coupon Bonds When Firm Values and Interest Rates are Stochastic

Mark C. W. Wong
Stewart D. Hodges

Financial Options Research Centre
Warwick Business School, University of Warwick,

This paper develops a flexible binomial approach to valuing risky debt when interest rates and firm values are stochastic. By using a hypothetical asset as a numeraire, it can be shown that not only does the use of this numeraire significantly simplify the analytic valuation of risky discount bonds, but also gives an implication that the computations of two-factor model can be implemented easily. By extending the method employed by Ho, Stapleton and Subrahmanyam (1995), we suggest an efficient computation algorithm for the pricing of general risky coupon bonds. We investigate the properties of defaultable bonds in an economy of stochastic interest rates. Interactions of market and credit risk are also discussed in this paper.

This approach has a number of interesting implications, including: Firstly, the recovery rate of a defaulted bond is generated endogenously depending on the remaining values of the firm. Secondly, our model integrates market and credit risk together to allow for a more complete picture of the underlying risks, as Longstaff and Schwartz (1995) provides strong evidence that both default risk and interest rate risk are necessary components for a valuation model for corporate debt. We show that when the firm value is low, its credit spread is more sensitive to the changes in interest rates. This confirms our intuition that firms with low credit quality should have more market risk than firms with high credit quality. Thirdly, while providing conceptual insights into default behaviour, the flexibility of our method allows for efficient pricing of bond options, credit risk put options on a general defaultable coupon bond and floating rate notes. Fourthly, this structural approach also paves the way for a further analysis of more complicated debt structures.