Pricing Vulnerable European Options under Lévy Process with Stochastic Volatility
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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2018/3402703 |
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| _version_ | 1832562087791951872 |
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| author | Chaoqun Ma Shengjie Yue Yishuai Ren |
| author_facet | Chaoqun Ma Shengjie Yue Yishuai Ren |
| author_sort | Chaoqun Ma |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ea15f2da5a544d71aff685878822cede |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-ea15f2da5a544d71aff685878822cede2025-02-03T01:23:29ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/34027033402703Pricing Vulnerable European Options under Lévy Process with Stochastic VolatilityChaoqun Ma0Shengjie Yue1Yishuai Ren2Business School of Hunan University, Changsha 410082, ChinaBusiness School of Hunan University, Changsha 410082, ChinaBusiness School of Hunan University, Changsha 410082, ChinaThis 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.http://dx.doi.org/10.1155/2018/3402703 |
| spellingShingle | Chaoqun Ma Shengjie Yue Yishuai Ren Pricing Vulnerable European Options under Lévy Process with Stochastic Volatility Discrete Dynamics in Nature and Society |
| title | Pricing Vulnerable European Options under Lévy Process with Stochastic Volatility |
| title_full | Pricing Vulnerable European Options under Lévy Process with Stochastic Volatility |
| title_fullStr | Pricing Vulnerable European Options under Lévy Process with Stochastic Volatility |
| title_full_unstemmed | Pricing Vulnerable European Options under Lévy Process with Stochastic Volatility |
| title_short | Pricing Vulnerable European Options under Lévy Process with Stochastic Volatility |
| title_sort | pricing vulnerable european options under levy process with stochastic volatility |
| url | http://dx.doi.org/10.1155/2018/3402703 |
| work_keys_str_mv | AT chaoqunma pricingvulnerableeuropeanoptionsunderlevyprocesswithstochasticvolatility AT shengjieyue pricingvulnerableeuropeanoptionsunderlevyprocesswithstochasticvolatility AT yishuairen pricingvulnerableeuropeanoptionsunderlevyprocesswithstochasticvolatility |