Calibration of the Volatility in Option Pricing Using the Total Variation Regularization
In market transactions, volatility, which is a very important risk measurement in financial economics, has significantly intimate connection with the future risk of the underlying assets. Identifying the implied volatility is a typical PDE inverse problem. In this paper, based on the total variation...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/510819 |
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| author | Yu-Hua Zeng Shou-Lei Wang Yu-Fei Yang |
| author_facet | Yu-Hua Zeng Shou-Lei Wang Yu-Fei Yang |
| author_sort | Yu-Hua Zeng |
| collection | DOAJ |
| description | In market transactions, volatility, which is a very important risk measurement in financial economics, has significantly intimate connection with the future risk of the underlying assets. Identifying the implied volatility is a typical PDE inverse problem. In this paper, based on the total variation regularization strategy, a bivariate total variation regularization model is proposed to estimate the implied volatility. We not only prove the existence of the solution, but also provide the necessary condition of the optimal control problem—Euler-Lagrange equation. The stability and convergence analyses for the proposed approach are also given. Finally, numerical experiments have been carried out to show the effectiveness of the method. |
| format | Article |
| id | doaj-art-9b0d008a62cc43bea2c716907e5aeeba |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-9b0d008a62cc43bea2c716907e5aeeba2025-02-03T01:01:03ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/510819510819Calibration of the Volatility in Option Pricing Using the Total Variation RegularizationYu-Hua Zeng0Shou-Lei Wang1Yu-Fei Yang2College of Mathematics and Econometrics, Hunan University, Changsha 410082, ChinaCollege of Mathematics and Econometrics, Hunan University, Changsha 410082, ChinaDepartment of Information and Computing Science, Changsha University, Changsha 410003, ChinaIn market transactions, volatility, which is a very important risk measurement in financial economics, has significantly intimate connection with the future risk of the underlying assets. Identifying the implied volatility is a typical PDE inverse problem. In this paper, based on the total variation regularization strategy, a bivariate total variation regularization model is proposed to estimate the implied volatility. We not only prove the existence of the solution, but also provide the necessary condition of the optimal control problem—Euler-Lagrange equation. The stability and convergence analyses for the proposed approach are also given. Finally, numerical experiments have been carried out to show the effectiveness of the method.http://dx.doi.org/10.1155/2014/510819 |
| spellingShingle | Yu-Hua Zeng Shou-Lei Wang Yu-Fei Yang Calibration of the Volatility in Option Pricing Using the Total Variation Regularization Journal of Applied Mathematics |
| title | Calibration of the Volatility in Option Pricing Using the Total Variation Regularization |
| title_full | Calibration of the Volatility in Option Pricing Using the Total Variation Regularization |
| title_fullStr | Calibration of the Volatility in Option Pricing Using the Total Variation Regularization |
| title_full_unstemmed | Calibration of the Volatility in Option Pricing Using the Total Variation Regularization |
| title_short | Calibration of the Volatility in Option Pricing Using the Total Variation Regularization |
| title_sort | calibration of the volatility in option pricing using the total variation regularization |
| url | http://dx.doi.org/10.1155/2014/510819 |
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