Pricing and Hedging Strategies of Vulnerable Black-Scholes Option on Defaultable Securities Subject to the Intersection of Market and Credit Risk

Abstract

This paper derives the pricing formulas and put-call parity for ＂hybrid options＂ -vulnerable options on defaultable securities-with the presence of the intersection of market and twofold default risk. Default intensities are modeled as a two-factor Cox process, and the dependency of option writers' default on the underlying stock default is also captured. We find counterparty risk generates credit discount on option value, while reference risk generates credit premium. The latter significantly dominates the former. The impact of twofold default risk on option hedging ratios fails to replicate consistency in the price pattern. The asymmetric behavior of option deltas with respect to reference risk is attributed to the trade-off between negative early-fixed effect and positive leverage effect. Also, our model generates a positive co-movement between these two types of default risk impact with varied choices of economic variables. Such a model feature reflects the empirical implication of credit contagion as well as the clustering of default.