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IMA Journal of Management Mathematics Advance Access originally published online on May 24, 2007
IMA Journal of Management Mathematics 2007 18(4):315-329; doi:10.1093/imaman/dpm021
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© The authors 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Pricing vulnerable European options with stochastic default barriers

CH Hui{dagger}

Research Department, Hong Kong Monetary Authority, 55th Floor, 8, Finance Street, Central, Hong Kong, China

CF Lo and KC Ku

Institute of Theoretical Physics and Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China

{dagger} Email: cho-hoi_hui{at}hkma.gov.hk

Received on 31 July 2006. Accepted on 15 March 2007.

This paper develops a valuation model of European options incorporating a stochastic default barrier, which extends a constant default barrier proposed in the Hull–White model. The default barrier is considered as an option writer's liability. Closed-form solutions of vulnerable European option values based on the model are derived to study the impact of the stochastic default barriers on option values. The numerical results show that negative correlation between the firm values and the stochastic default barriers of option writers gives material reductions in option values where the options are written by firms with leverage ratios corresponding to BBB or BB ratings.

Keywords: option pricing; credit risk; derivatives


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