Pricing Vulnerable Black-Scholes Options with Dynamic Default Barriers

by Cho-Hoi Hui of the Hong Kong Monetary Authority,
Chi-Fai Lo of the Chinese University of Hong Kong, and
Hon Chor Lee of the Chinese University of Hong Kong

Summer 2003

Abstract: This paper develops a valuation model of European Black-Scholes options incorporating a dynamic default barrier. Different default scenarios can be incorporated into the valuation model through adjusting the default barrier's dynamics. The closed-form solutions of vulnerable European option values based on the model are derived to study the impact of the dynamic default barrier on option prices. The pricing solution for a call option is used to obtain option prices with the default barriers proposed in the Briys and de Varenne model and the Longstaff and Schwartz model respectively. The numerical results show that different default scenarios implied from the dynamic default barrier have material impact on option prices.

JEL Classification: G13.

Keywords: Option pricing, Credit risk, Derivatives.

Published in: Journal of Derivatives, Vol. 10, No. 4, (Summer 2003), pp. 62-69.

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