Option Pricing under the Subordinated Market Models
This paper aims to study option pricing problem under the subordinated Brownian motion. Firstly, we prove that the subordinated Brownian motion controlled by the fractional diffusion equation has many financial properties, such as self-similarity, leptokurtic, and long memory, which indicate that th...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2022/6213803 |
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| _version_ | 1832566183790903296 |
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| author | Longjin Lv Changjuan Zheng Luna Wang |
| author_facet | Longjin Lv Changjuan Zheng Luna Wang |
| author_sort | Longjin Lv |
| collection | DOAJ |
| description | This paper aims to study option pricing problem under the subordinated Brownian motion. Firstly, we prove that the subordinated Brownian motion controlled by the fractional diffusion equation has many financial properties, such as self-similarity, leptokurtic, and long memory, which indicate that the fractional calculus can describe the financial data well. Then, we investigate the option pricing under the assumption that the stock price is driven by the subordinated Brownian motion. The closed-form pricing formula for European options is derived. In the comparison with the classic Black–Sholes model, we find the option prices become higher, and the “volatility smiles” phenomenon happens in the proposed model. Finally, an empirical analysis is performed to show the validity of these results. |
| format | Article |
| id | doaj-art-219fc981d4f44e3ba5273ef2b0974a88 |
| institution | Kabale University |
| issn | 1607-887X |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-219fc981d4f44e3ba5273ef2b0974a882025-02-03T01:04:45ZengWileyDiscrete Dynamics in Nature and Society1607-887X2022-01-01202210.1155/2022/6213803Option Pricing under the Subordinated Market ModelsLongjin Lv0Changjuan Zheng1Luna Wang2School of Finance and InformationSchool of Finance and InformationSchool of Finance and InformationThis paper aims to study option pricing problem under the subordinated Brownian motion. Firstly, we prove that the subordinated Brownian motion controlled by the fractional diffusion equation has many financial properties, such as self-similarity, leptokurtic, and long memory, which indicate that the fractional calculus can describe the financial data well. Then, we investigate the option pricing under the assumption that the stock price is driven by the subordinated Brownian motion. The closed-form pricing formula for European options is derived. In the comparison with the classic Black–Sholes model, we find the option prices become higher, and the “volatility smiles” phenomenon happens in the proposed model. Finally, an empirical analysis is performed to show the validity of these results.http://dx.doi.org/10.1155/2022/6213803 |
| spellingShingle | Longjin Lv Changjuan Zheng Luna Wang Option Pricing under the Subordinated Market Models Discrete Dynamics in Nature and Society |
| title | Option Pricing under the Subordinated Market Models |
| title_full | Option Pricing under the Subordinated Market Models |
| title_fullStr | Option Pricing under the Subordinated Market Models |
| title_full_unstemmed | Option Pricing under the Subordinated Market Models |
| title_short | Option Pricing under the Subordinated Market Models |
| title_sort | option pricing under the subordinated market models |
| url | http://dx.doi.org/10.1155/2022/6213803 |
| work_keys_str_mv | AT longjinlv optionpricingunderthesubordinatedmarketmodels AT changjuanzheng optionpricingunderthesubordinatedmarketmodels AT lunawang optionpricingunderthesubordinatedmarketmodels |