Pricing Vulnerable Black-Scholes Options with Dynamic Default Barriers

Abstract

The “structural approach” to modeling credit risk specifies a stochastic process that the net asset value of the issuing firm is assumed to follow. If firm value falls below a certain “default barrier,” bankruptcy is triggered and the firm is assumed to default on its vulnerable obligations. In this article, Hui, Lo, and Lee apply the methodology to price vulnerable options written by a default risky firm. They show how a variety of default scenarios may be accommodated by use of a dynamic default barrier, while maintaining a closed-form valuation equation.