Pricing of American Carbon Emission Derivatives and Numerical Method under the Mixed Fractional Brownian Motion
This paper studies the pricing of American carbon emission derivatives and its numerical method under the mixed fractional Brownian motion. To capture the long memory properties such as self-similarity and long-range dependence in the price process, we proposed a model based on a fractional Black–Sc...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2021/6612284 |
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| author | Yuling Wang Jing Wang |
| author_facet | Yuling Wang Jing Wang |
| author_sort | Yuling Wang |
| collection | DOAJ |
| description | This paper studies the pricing of American carbon emission derivatives and its numerical method under the mixed fractional Brownian motion. To capture the long memory properties such as self-similarity and long-range dependence in the price process, we proposed a model based on a fractional Black–Scholes, which is more in line with the actual characteristics of the option market. We have outlined a power penalty approach using parabolic variation inequality and linear complementarity (LCP) which arises from mixed fractional Brownian motion. In addition, we introduced a nonuniform grid-based modification of the fitted finite volume method for numerical solution. Numerically, we show the impact of Hurst exponent on the pricing and analyze the convergence rates of the proposed penalty method. In conclusion, since mfBm is a well-developed mathematical model of strongly correlated stochastic processes, this model will be an efficient model for pricing carbon financial derivative. |
| format | Article |
| id | doaj-art-3329b4c2df4d40288492c8b711c8f8fb |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-3329b4c2df4d40288492c8b711c8f8fb2025-02-03T01:01:25ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2021-01-01202110.1155/2021/66122846612284Pricing of American Carbon Emission Derivatives and Numerical Method under the Mixed Fractional Brownian MotionYuling Wang0Jing Wang1School of Economics, South-Central University for Nationalities, Wuhan 430074, ChinaSchool of Management Science and Engineering, Anhui University of Finance and Economics, Anhui, Bengbu 233030, ChinaThis paper studies the pricing of American carbon emission derivatives and its numerical method under the mixed fractional Brownian motion. To capture the long memory properties such as self-similarity and long-range dependence in the price process, we proposed a model based on a fractional Black–Scholes, which is more in line with the actual characteristics of the option market. We have outlined a power penalty approach using parabolic variation inequality and linear complementarity (LCP) which arises from mixed fractional Brownian motion. In addition, we introduced a nonuniform grid-based modification of the fitted finite volume method for numerical solution. Numerically, we show the impact of Hurst exponent on the pricing and analyze the convergence rates of the proposed penalty method. In conclusion, since mfBm is a well-developed mathematical model of strongly correlated stochastic processes, this model will be an efficient model for pricing carbon financial derivative.http://dx.doi.org/10.1155/2021/6612284 |
| spellingShingle | Yuling Wang Jing Wang Pricing of American Carbon Emission Derivatives and Numerical Method under the Mixed Fractional Brownian Motion Discrete Dynamics in Nature and Society |
| title | Pricing of American Carbon Emission Derivatives and Numerical Method under the Mixed Fractional Brownian Motion |
| title_full | Pricing of American Carbon Emission Derivatives and Numerical Method under the Mixed Fractional Brownian Motion |
| title_fullStr | Pricing of American Carbon Emission Derivatives and Numerical Method under the Mixed Fractional Brownian Motion |
| title_full_unstemmed | Pricing of American Carbon Emission Derivatives and Numerical Method under the Mixed Fractional Brownian Motion |
| title_short | Pricing of American Carbon Emission Derivatives and Numerical Method under the Mixed Fractional Brownian Motion |
| title_sort | pricing of american carbon emission derivatives and numerical method under the mixed fractional brownian motion |
| url | http://dx.doi.org/10.1155/2021/6612284 |
| work_keys_str_mv | AT yulingwang pricingofamericancarbonemissionderivativesandnumericalmethodunderthemixedfractionalbrownianmotion AT jingwang pricingofamericancarbonemissionderivativesandnumericalmethodunderthemixedfractionalbrownianmotion |