Fractional Order Stochastic Differential Equation with Application in European Option Pricing
Memory effect is an important phenomenon in financial systems, and a number of research works have been carried out to study the long memory in the financial markets. In recent years, fractional order ordinary differential equation is used as an effective instrument for describing the memory effect...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/621895 |
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| _version_ | 1832552854652452864 |
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| author | Qing Li Yanli Zhou Xinquan Zhao Xiangyu Ge |
| author_facet | Qing Li Yanli Zhou Xinquan Zhao Xiangyu Ge |
| author_sort | Qing Li |
| collection | DOAJ |
| description | Memory effect is an important phenomenon in financial systems, and a number of research works have been carried out to study the long memory in the financial markets. In recent years, fractional order ordinary differential equation is used as an effective instrument for describing the memory effect in complex systems. In this paper, we establish a fractional order stochastic differential equation (FSDE) model to describe the effect of trend memory in financial pricing. We, then, derive a European option pricing formula based on the FSDE model and prove the existence of the trend memory (i.e., the mean value function) in the option pricing formula when the Hurst index is between 0.5 and 1. In addition, we make a comparison analysis between our proposed model, the classic Black-Scholes model, and the stochastic model with fractional Brownian motion. Numerical results suggest that our model leads to more accurate and lower standard deviation in the empirical study. |
| format | Article |
| id | doaj-art-6172ffea2a8c4d7f8384f867426b75be |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-6172ffea2a8c4d7f8384f867426b75be2025-02-03T05:57:41ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/621895621895Fractional Order Stochastic Differential Equation with Application in European Option PricingQing Li0Yanli Zhou1Xinquan Zhao2Xiangyu Ge3School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, ChinaSchool of Finance, Zhongnan University of Economics and Law, Wuhan 430073, ChinaSchool of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, ChinaSchool of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, ChinaMemory effect is an important phenomenon in financial systems, and a number of research works have been carried out to study the long memory in the financial markets. In recent years, fractional order ordinary differential equation is used as an effective instrument for describing the memory effect in complex systems. In this paper, we establish a fractional order stochastic differential equation (FSDE) model to describe the effect of trend memory in financial pricing. We, then, derive a European option pricing formula based on the FSDE model and prove the existence of the trend memory (i.e., the mean value function) in the option pricing formula when the Hurst index is between 0.5 and 1. In addition, we make a comparison analysis between our proposed model, the classic Black-Scholes model, and the stochastic model with fractional Brownian motion. Numerical results suggest that our model leads to more accurate and lower standard deviation in the empirical study.http://dx.doi.org/10.1155/2014/621895 |
| spellingShingle | Qing Li Yanli Zhou Xinquan Zhao Xiangyu Ge Fractional Order Stochastic Differential Equation with Application in European Option Pricing Discrete Dynamics in Nature and Society |
| title | Fractional Order Stochastic Differential Equation with Application in European Option Pricing |
| title_full | Fractional Order Stochastic Differential Equation with Application in European Option Pricing |
| title_fullStr | Fractional Order Stochastic Differential Equation with Application in European Option Pricing |
| title_full_unstemmed | Fractional Order Stochastic Differential Equation with Application in European Option Pricing |
| title_short | Fractional Order Stochastic Differential Equation with Application in European Option Pricing |
| title_sort | fractional order stochastic differential equation with application in european option pricing |
| url | http://dx.doi.org/10.1155/2014/621895 |
| work_keys_str_mv | AT qingli fractionalorderstochasticdifferentialequationwithapplicationineuropeanoptionpricing AT yanlizhou fractionalorderstochasticdifferentialequationwithapplicationineuropeanoptionpricing AT xinquanzhao fractionalorderstochasticdifferentialequationwithapplicationineuropeanoptionpricing AT xiangyuge fractionalorderstochasticdifferentialequationwithapplicationineuropeanoptionpricing |