Vulnerable option risky corporate bond and credit spread

Abstract

The focus of credit risk analysis has been either on valuation of risky corporate bond and credit spread, or valuation of vulnerable options in separate contexts. There are two main draw backs associated with existing studies. First, corporate bonds and credit spread are generally analyzed in a context where corporate debt is the only liability of the firm and firm's value follows a continuous stochastic process. This set-up implies a zero short term spread, which is strongly rejected by empirical observations. Such an implication may be attributed to the simplified assumption on corporate liabilities. Since a corporation generally bas more than one type of liabilities, modelling multiple liabilities may help to incorporate discontinuity in firm's value and hence eliminate such implications. Second, vulnerable options arc priced under the assumption that firm can fully payoff the option if firm's value is above the default, barrier at, option's maturity. Such assumption is not realistic since a corporation can find itself in a solvent position at option's maturity but with assets insufficient to payoff the option. The main contribution of this study is to overcome these two shortcomings. The proposed framework extends the existing equity-bond capital structure to equity-bond-derivative setting. The firm under study has two types of liabilities: a corporate bond and a short position in options. Risky corporate bond, credit spread and vulnerable options are analyzed. Numerical exercises illustrate that adding a derivative type of liability can lead to positive short term credit spreads and various shapes of credit spread term structures. In addition, as a surprising result we find that vulnerable options need not always be worth less than their default free counterparts. Moreover, it is not always in the best interest of option holders to impose a strict covenant.