The Impact of Credit Risk on Equity Options

Abstract

The aim of this work is to understand and measure to what extent equity options price credit risk. With the exception of Toft and Prucyk (1997), which is a dated work based on the simplistic assumption of a reference company issuing perpetual debt, all the work in the literature which try to establish a link between the credit default swaps and equity options rely on reduced-form models (Carr and Linetsky 2006, Carr and Wu 2010, Carr et al. 2010). Thus, the connection between the firm's fundamentals and the pricing of these derivative contracts are ignored. With a novel structural model, which stems from Geske (1977, 1979), equity is priced as a compound call option written on the firm's asset. The proposed structural model is first able to reconcile some puzzling findings documented by Carrand Wu (2017) on increasing leverage due to increasing business risk. Moreover, as the price equity options is shown to depends on the probability of the option expiring in-the-money, conditional on the firm's survival, this decomposition allows to construct a new measure of impact of credit risk on options. It is then shown that put options, contrary to calls, are sensitive to changes in the default risk in the underlying company. In addition, this measure is able to forecast future changes of the negative skew of long-term maturity options written on the equity of the same company. Finally, I show that the implied volatilities estimated \'a la Black-Scholes tend to average out the effect of credit risk over the moneyness space, leading to potential biases when applied for risk management purposes.