Does default risk in coupons affect the valuation of corporate bonds?: a contingent claims model - Financial Distress Special Issue

Financial Management (Financial Management Association), Autumn, 1993 by Joon Kim, Krishna Ramaswamy, Suresh Sundaresan

6. S. Brown and P. Dybvig, "The Empirical Implications of the Cox, Ingersoll, Ross Theory of the Term Structure of Interest," Journal of Finance (July 1986), pp. 617-632.

7. J.C. Cox, J.E. Ingersoll, Jr., and S.A. Ross, "Duration and the Measurement of Basis Risk," Journal of Business (January 1979), pp. 51-61.

8. J.C. Cox, J.E. Ingersoll, Jr., and S.A. Ross, "A Theory of the Term Structure of Interest Rates," Econometrica (March 1985), pp. 385-407. In their pioneering papers, Black and Scholes |3~ and Merton |17~ emphasized the correspondence between corporate liabilities and options, and indicated how the theory of option pricing might be used to value corporate liabilities. This correspondence has been the cornerstone of a number of studies: Merton |18~ examined the risk structure of interest rates; Black and Cox |2~ provided significant extensions by explicitly modeling some indenture provisions; and Brennan and Schwartz |5~ and Ingersoll |14~ used this correspondence to value convertible and callable corporate liabilities. This list is only partial, but it illustrates the range of issues which may be addressed using option pricing theory.

While the insights offered by this research are beyond questioning, the ability of this approach to explain the yield spreads between corporate bonds and comparable default-free Treasury bonds has been questioned in recent papers. In a paper which is closely related to our work, Jones, Mason, and Rosenfeld |16~ sought to test the predictive power of a contingent claims pricing model based on some simplifying assumptions which included non-stochastic interest rates, strict "me-first" rules, and the sale of assets to fund bond-related payments; they also permitted interaction of multiple call and sinking fund provisions. The empirical findings of Jones, Mason, and Rosenfeld |16~ indicate that such versions of contingent claims pricing models do not generate the levels of yield spreads which one observes in practice.(1) Over the 1926-1986 period, the yield spreads on high-grade corporates (AAA-rated) ranged from 15 to 215 basis points and averaged 77 basis points; and the yield spreads on BAAs (also investment-grade) ranged from 51 to 787 basis points and averaged 198 basis points. We show later in this paper that the conventional contingent claims model due to Merton |18~ is unable to generate default premiums in excess of 120 basis points, even when excessive debt ratios and volatility parameters are used in the numerical simulation.

The inability (at plausible parameter values) of contingent claims pricing models to account for the magnitude of the yield spreads between corporate and Treasury bonds provides the motivation for this paper. The focus is on two issues central to the valuation of corporate claims.

First, we make explicit assumptions about how and when bankruptcy occurs and we discuss the nature of the payoffs with regard to indenture provisions. Previous studies have generally placed the burden of bankruptcy on the principal payment at maturity, and not on the coupon obligations along the way. Our focus, in contrast, is on (i) the possibility of the firm defaulting on its coupon obligations, and on (ii) the interaction between dividends and default risk.

Second, the values of Treasury and corporate bonds are influenced significantly by interest rate risk: Jones, Mason, and Rosenfeld |16~ concluded that the introduction of stochastic interest rates might improve the performance of contingent claims pricing models. We model this source of uncertainty by specifying a stochastic process for the evolution of the short rate. We find that although the yields on both Treasury and corporate issues are significantly influenced by the uncertainty in interest rates, the yield spreads are quite insensitive to interest rate uncertainty. The role of call features in corporate and Treasury bonds is also studied. The call feature has a differential effect on Treasury issues relative to corporate issues: we find that the call feature is relatively more valuable in Treasury issues than it is in corporate issues. The differential effect of call provisions is a significant factor in explaining the observed yield spreads between noncallable ("straight") corporates and straight Treasuries on the one hand and callable corporates and callable Treasuries on the other.

Our paper, by incorporating these features in a simple partial equilibrium setting, makes two contributions. First, it builds a contingent claims model with stochastic interest rates to accommodate the risk of default in the coupons in the presence of dividends, and examines the effect of the call provision in this more realistic setting. Second, it provides evidence that these models are capable of generating yield spreads that are consistent with the levels observed in practice. To be sure, all the models presented here describe firms with extremely simple capital structures -- firms with a single issue of debt outstanding. Given the results, however, we are hopeful that contingent claims models will be useful in studying the more complex liabilities of firms with complicated capital structures.(2)