DOES DEFAULT RISK IN COUPONS AFFECT THE VALUATION OF CORPORATE-BONDS - A CONTINGENT CLAIMS MODEL

In their pioneering papers, Black and Scholes [3] and Merton [ 17] emp hasized the coffespondence 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 comerstone of a number of studies: Merton [ 1 8] examined the risk structure of inte rest rates; Black and Cox [2] provided significant extensions by expli citly 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 illu strates the range of issues which may be addressed using option pricin g theory. While the insights offered by this research are beyond quest ioning, the ability of this approach to explain the yield spreads betw een corporate bonds and comparable default-fi-ee Treasury bonds has be en questioned in recent papers. In a paper which is closely related to our work, Jones, Mason, and Rosenfeld [16] sought to test the predict ive power of a contingent claims pricing model based on some simplifyi ng assumptions which included nonstochastic interest rates, strict ''m e-first'' rules, and the sale of assets to fund bond-related payments; they also permitted interaction of multiple call and sinking fund pro visions. The empirical findings of Jones, Mason, and Rosenfeld [16] in dicate that such versions of contingent claims pricing models do n6t g enerate the levels of yield spreads which one observes in practice.1 O ver the 1926-1986 period, the yield spreads on high-grade corporates ( AAA-rated) ranged from 15 to 215 basis points and averaged 77 basis po ints; and the yield spreads on BAAs (also investment-grade) ranged fro m 51 to 787 basis points and averaged 198 basis points. We show later in this paper that the conventional contingent claims model due to Mer ton [18] is unable to generate default premium s in excess of 120 basi s points, even when excessive debt ratios and volatility parameters ar e used in the numerical simulation. The inability (at plausible parame ter values) of contingent claims pricing models to account for the mag nitude of the yield spreads between corporate and Treasury bonds provi des the motivation for this paper. The focus is on two issues central to the valuation of corporate claims. First, we make explicit assumpti ons 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 i nfluenced significantly by interest rate risk: Jones, Mason, and Rosen feld [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 f or the evolution of the short rate. We find that although the yields o n both Treasury and corporate issues are significantly influenced by t he uncertainty in interest rates, the yield spreads are quite insensit ive to interest rate uncertainty. The role of call features in corpora te and Treasury bonds is also studied. The call feature has a differen tial effect on Treasury issues relative to corporate issues: we find t hat the call feature is relatively more valuable in Treasury issues th an it is in corporate issues. The differential effect of call provisio ns is a significant factor in explaining the observed yield spreads be tween noncallable (''straight'') corporates and straight Treasuries on the one hand and callable corporates and callable Treasuries on the o ther. Our paper, by incorporating these features in a simple partial e quilibrium setting, makes two contributions. First, it builds a contin gent claims model with stochastic interest rates to accommodate the ri sk of default in the coupons in the presence of dividends, and examine s the effect of the call provision in this more realistic setting. Sec ond, 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 extrem ely simple capital structuresfirms with a single issue of debt outstan ding. Given the results, however, we are hopeful that contingent claim s models will be useful in studying the more complex liabilities of fi rms with complicated capital structures.2 The paper is organized as fo llows. In Section I, we build the contingent claims valuation framewor k for pricing corporate and Treasury bonds. We discuss the differences between the models we study and the model in Merton [18]. Section II provides a numerical analysis of straight noncallable corporate and Tr easury bonds. We characterize the behavior of yield spreads with respe ct to changes in maturity, with respect to shifts in the debt ratios o f the firm, and with respect to the parameters that govem the stochast ic process that drives interest rates. In Section III, we extend the m odel to callable bonds and examine optimal call policies in a stochast ic term structure environment. We conclude the paper in Section IV.