Valuation of the Vulnerable Option Price Based on Mixed Fractional Brownian Motion
The pricing problem of a kind of European vulnerable option was studied. The mixed fractional Brownian motion and the jump process were used to characterize the evolution of stock prices. The closed-form solution to European option pricing was obtained by applying martingale measure transformation m...
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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/10.1155/2018/4047350 |
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| _version_ | 1832545404927868928 |
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| author | Yanmin Ouyang Jingyuan Yang Shengwu Zhou |
| author_facet | Yanmin Ouyang Jingyuan Yang Shengwu Zhou |
| author_sort | Yanmin Ouyang |
| collection | DOAJ |
| description | The pricing problem of a kind of European vulnerable option was studied. The mixed fractional Brownian motion and the jump process were used to characterize the evolution of stock prices. The closed-form solution to European option pricing was obtained by applying martingale measure transformation method. At the end of this paper, some numerical experiments were adopted to compare the new pricing formula introduced in this paper with the classical Black-Scholes pricing formula. The result showed that the new pricing formula conformed to the actual financial market. In fact, the option value is positively correlated with the underlying asset price and the company’s asset price and the jump process has significant influence on the value of option. |
| format | Article |
| id | doaj-art-dee796dbc69f427b95bdc9267a156963 |
| 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-dee796dbc69f427b95bdc9267a1569632025-02-03T07:26:05ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/40473504047350Valuation of the Vulnerable Option Price Based on Mixed Fractional Brownian MotionYanmin Ouyang0Jingyuan Yang1Shengwu Zhou2School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, ChinaSchool of Management, China University of Mining and Technology, Xuzhou, 221116, ChinaSchool of Mathematics, China University of Mining and Technology, Xuzhou, 221116, ChinaThe pricing problem of a kind of European vulnerable option was studied. The mixed fractional Brownian motion and the jump process were used to characterize the evolution of stock prices. The closed-form solution to European option pricing was obtained by applying martingale measure transformation method. At the end of this paper, some numerical experiments were adopted to compare the new pricing formula introduced in this paper with the classical Black-Scholes pricing formula. The result showed that the new pricing formula conformed to the actual financial market. In fact, the option value is positively correlated with the underlying asset price and the company’s asset price and the jump process has significant influence on the value of option.http://dx.doi.org/10.1155/2018/4047350 |
| spellingShingle | Yanmin Ouyang Jingyuan Yang Shengwu Zhou Valuation of the Vulnerable Option Price Based on Mixed Fractional Brownian Motion Discrete Dynamics in Nature and Society |
| title | Valuation of the Vulnerable Option Price Based on Mixed Fractional Brownian Motion |
| title_full | Valuation of the Vulnerable Option Price Based on Mixed Fractional Brownian Motion |
| title_fullStr | Valuation of the Vulnerable Option Price Based on Mixed Fractional Brownian Motion |
| title_full_unstemmed | Valuation of the Vulnerable Option Price Based on Mixed Fractional Brownian Motion |
| title_short | Valuation of the Vulnerable Option Price Based on Mixed Fractional Brownian Motion |
| title_sort | valuation of the vulnerable option price based on mixed fractional brownian motion |
| url | http://dx.doi.org/10.1155/2018/4047350 |
| work_keys_str_mv | AT yanminouyang valuationofthevulnerableoptionpricebasedonmixedfractionalbrownianmotion AT jingyuanyang valuationofthevulnerableoptionpricebasedonmixedfractionalbrownianmotion AT shengwuzhou valuationofthevulnerableoptionpricebasedonmixedfractionalbrownianmotion |