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Discrete Dynamics in Nature and Society
Volume 2018, Article ID 3402703, 16 pages
https://doi.org/10.1155/2018/3402703
Research Article

Pricing Vulnerable European Options under Lévy Process with Stochastic Volatility

Business School of Hunan University, Changsha 410082, China

Correspondence should be addressed to Shengjie Yue; moc.361@81eijgnehseuy

Received 5 July 2018; Accepted 30 September 2018; Published 23 October 2018

Academic Editor: Daniel Sevcovic

Copyright © 2018 Chaoqun Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper considers the pricing issue of vulnerable European option when the dynamics of the underlying asset value and counterparty’s asset value follow two correlated exponential Lévy processes with stochastic volatility, and the stochastic volatility is divided into the long-term and short-term volatility. A mean-reverting process is introduced to describe the common long-term volatility risk in underlying asset price and counterparty’s asset value. The short-term fluctuation of stochastic volatility is governed by a mean-reverting process. Based on the proposed model, the joint moment generating function of underlying log-asset price and counterparty’s log-asset value is explicitly derived. We derive a closed-form solution for the vulnerable European option price by using the Fourier inversion formula for distribution functions. Finally, numerical simulations are provided to illustrate the effects of stochastic volatility, jump risk, and counterparty credit risk on the vulnerable option price.