Pricing Black-Scholes options with correlated interest rate risk and credit risk: an extension

摘要

This article provides a closed-form valuation formula for the Black-Scholes options subject to interest rate risk and credit risk. Not only does our model allow for the possible default of the option issuer prior to the option's maturity, but also considers the correlations among the option issuer's total assets, the underlying stock, and the default-free zero coupon bond. We further tailor-make a specific credit-linked option for hedging the default risk of the option issuer. The numerical results show that the default risk of the option issuer significantly reduces the option values, and the vulnerable option values may be remarkably overestimated in the case where the default can occur only at the maturity of the option.