Pricing Vulnerable Options with Correlated Credit Risk Under Jump-Diffusion Processes

摘要

This study extends the framework of Klein [Journal of Banking & Finance, 20, 1211-1229] to price vulnerable options. We provide a pricing model for vulnerable options which face not only default risk but also rare shocks encountered by the underlying asset and the assets of the counterparty. The dynamics of asset prices are governed by jump-diffusions with two sorts of assets correlated with each other. Jumps are divided into idiosyncratic component for each asset price and systematic component affecting the prices of all assets. A closed-form valuation formula is derived for vulnerable European options. Numerical analysis compares the results of this model with those of other pricing formulae, and illustrates jump effects on the vulnerable option prices.