The pricing of corporate debt and related issues

Abstract

The purpose of this thesis is to study the pricing and credit risk of corporate debt using structural and reduced-form approaches. We discuss the theoretical aspects of three important topics in pricing risky debt: (i) the impact of stochastic interest rates, and hence the interaction between market risk and credit risk; (ii) the impact of diversifiable and non-diversifiable jump risks on pricing and default mechanisms, and (iii) a reduced-form model with a firm’s fundamental variables. To investigate the relationships between market risk and credit risk, we develop a flexible binomial framework for valuing credit-sensitive instruments by generalizing the valuation model of Geske [1977]. We price a defaultable coupon bond when interest rates and a firm’s asset value are stochastic. Our results confirm our belief that firms with low credit quality should have more market risk than firms with high credit quality. We discuss the implications of the results for capital adequacy. In addition to providing conceptual insights into the default behaviour, the flexibility of our method allows for efficient pricing of other credit-sensitive instruments. To improve the short-end properties of credit spreads, we model a firm’s asset value as a jump-diffusion process. We show several significant implications of the jump process for the term structure of credit spreads. We also discuss the effects of the disversifiability of jumps on corporate debt pricing. We prove that without considering systematic jump risk, theoretical models tend to underestimate credit spreads. Another contribution of this thesis is the incorporation of taxes into our model to show that taxes do have significant effects on levels of credit spread. Interestingly, the model implies that a decrease in the federal tax rate may precipitate an earlier default of low-grade bonds. Finally, we investigate a reduced-form model of corporate debt, by taking into account stochastic interest rates, a firm’s equity values, and hazard rates of default. Through a moving average of a log-transformation of equity prices, we introduce structural characteristics of the firm into the model. This is an innovation