Pricing Vulnerable European Options under Lévy Process with Stochastic Volatility. (23rd October 2018)

• Record Type: Journal Article
• Authors: Ma, Chaoqun; Yue, Shengjie; Ren, Yishuai
• Other Names: Sevcovic Daniel Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2018(2018)
• Publication Date: 2018-10-23
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2018/3402703
• Languages: English
• ISSNs: 1026-0226

Abstract

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.