Pricing Black-Scholes options with correlated credit risk

This paper presents an improved method of pricing vulnerable Black-Scholes options under assumptions which are appropriate in many business situations. An analytic pricing formula is derived which allows not only for correlation between the option's underlying asset and the credit risk of the counterparty, but also for the option writer to have other liabilities. Further, the proportion of nominal claims paid out in default is endogenous to the model and is based on the terminal value of the assets of the counterparty and the amount of other equally ranking claims. Numerical examples compare the results of this model with those of other pricing formulas based on alternative assumptions, and illustrate how the model can be calibrated using market data.