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

Authors

  • Lihui Tian,

    1. Lihui Tian and Guanying Wang are at the Institute of Finance and Development, Nankai University, Tianjin, China
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  • Guanying Wang,

    1. Lihui Tian and Guanying Wang are at the Institute of Finance and Development, Nankai University, Tianjin, China
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  • Xingchun Wang,

    Corresponding author
    1. Xingchun Wang and Yongjin Wang are at the School of Mathematical Sciences and LPMC, Nankai University, Tianjin, China
    2. Xingchun Wang is also at the Mathematical Institute, University of Oxford, Oxford, UK
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  • Yongjin Wang

    1. Xingchun Wang and Yongjin Wang are at the School of Mathematical Sciences and LPMC, Nankai University, Tianjin, China
    2. Yongjin Wang is also at the School of Business, Nankai University, Tianjin, China
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  • The authors are grateful to the anonymous referee and the editor, Robert I. Webb, for their valuable comments and suggestions. All errors are our own. This work was supported by National Natural Science Foundation of China (No. 71272179 and No. 11271203). L. Tian was supported by “Program for New Century Excellent Talents in University” of the Ministry of Education in China. X. Wang was also supported by the China Scholarship Council (CSC, File No. 201206200026) and the Ministry of Education of China under a Scholarship Award for Excellent Doctoral Student.

Abstract

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. © 2013 Wiley Periodicals, Inc. Jrl Fut Mark 34:957–979, 2014

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