Convergence analysis of option drift rate inverse problem based on degenerate parabolic equation
In this paper, we study the convergence of the inverse drift rate problem of option pricing based on degenerate parabolic equations, aiming to recover the stock price drift rate function by known option market prices. Unlike the classical inverse parabolic equation problem, the article transforms th...
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| Language: | English |
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Elsevier
2025-05-01
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| Series: | Results in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037425000251 |
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| author | Miao-miao Song Zui-cha Deng Xiang Li Qiu Cui |
| author_facet | Miao-miao Song Zui-cha Deng Xiang Li Qiu Cui |
| author_sort | Miao-miao Song |
| collection | DOAJ |
| description | In this paper, we study the convergence of the inverse drift rate problem of option pricing based on degenerate parabolic equations, aiming to recover the stock price drift rate function by known option market prices. Unlike the classical inverse parabolic equation problem, the article transforms the original problem into an inverse problem with principal coefficients of the degenerate parabolic equation over a bounded region by variable substitution, thus avoiding the error introduced by artificial truncation. Under the optimal control framework, the problem is transformed into an optimization problem, the existence of the minimal solution is proved, and a mathematical proof of the convergence of the optimal solution is given. Finally, the gradient-type iterative method is applied to obtain the numerical solution of the inverse problem, and numerical experiments are conducted to verify it. This study provides an effective theoretical framework and numerical method for inferring the stock price drift rate from the option market price. |
| format | Article |
| id | doaj-art-63a2a9325f244c2cba07f9de335573bc |
| institution | Kabale University |
| issn | 2590-0374 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj-art-63a2a9325f244c2cba07f9de335573bc2025-08-20T03:52:24ZengElsevierResults in Applied Mathematics2590-03742025-05-012610056110.1016/j.rinam.2025.100561Convergence analysis of option drift rate inverse problem based on degenerate parabolic equationMiao-miao Song0Zui-cha Deng1Xiang Li2Qiu Cui3Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, People’s Republic of China; State Key Laboratory of Microbial Technology (Institute of Microbiological Technology), Shandong University, Qingdao, Shandong 266237, People’s Republic of China; Corresponding author at: Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, People’s Republic of China.Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, People’s Republic of China; Institute of Engineering Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, People’s Republic of ChinaDepartment of Materials Science, Fudan University, Yangpu District, Shanghai 200438, People’s Republic of ChinaState Key Laboratory of Microbial Technology (Institute of Microbiological Technology), Shandong University, Qingdao, Shandong 266237, People’s Republic of China; Corresponding author.In this paper, we study the convergence of the inverse drift rate problem of option pricing based on degenerate parabolic equations, aiming to recover the stock price drift rate function by known option market prices. Unlike the classical inverse parabolic equation problem, the article transforms the original problem into an inverse problem with principal coefficients of the degenerate parabolic equation over a bounded region by variable substitution, thus avoiding the error introduced by artificial truncation. Under the optimal control framework, the problem is transformed into an optimization problem, the existence of the minimal solution is proved, and a mathematical proof of the convergence of the optimal solution is given. Finally, the gradient-type iterative method is applied to obtain the numerical solution of the inverse problem, and numerical experiments are conducted to verify it. This study provides an effective theoretical framework and numerical method for inferring the stock price drift rate from the option market price.http://www.sciencedirect.com/science/article/pii/S2590037425000251Inverse problemsConvergenceOptimal controlNumerical algorithms |
| spellingShingle | Miao-miao Song Zui-cha Deng Xiang Li Qiu Cui Convergence analysis of option drift rate inverse problem based on degenerate parabolic equation Results in Applied Mathematics Inverse problems Convergence Optimal control Numerical algorithms |
| title | Convergence analysis of option drift rate inverse problem based on degenerate parabolic equation |
| title_full | Convergence analysis of option drift rate inverse problem based on degenerate parabolic equation |
| title_fullStr | Convergence analysis of option drift rate inverse problem based on degenerate parabolic equation |
| title_full_unstemmed | Convergence analysis of option drift rate inverse problem based on degenerate parabolic equation |
| title_short | Convergence analysis of option drift rate inverse problem based on degenerate parabolic equation |
| title_sort | convergence analysis of option drift rate inverse problem based on degenerate parabolic equation |
| topic | Inverse problems Convergence Optimal control Numerical algorithms |
| url | http://www.sciencedirect.com/science/article/pii/S2590037425000251 |
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