An Analysis of Asymptotic Properties and Error Control under the Exponential Jump-Diffusion Model for American Option Pricing
Our work is aimed at modeling the American option price by combining the dynamic programming and the optimal stopping time under two asset price models. In doing so, we attempt to control the theoretical error and illustrate the asymptotic characteristics of each model; thus, using a numerical illus...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/1049907 |
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| _version_ | 1832561399191044096 |
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| author | Mohamed Maidoumi Boubker Daafi Mehdi Zahid |
| author_facet | Mohamed Maidoumi Boubker Daafi Mehdi Zahid |
| author_sort | Mohamed Maidoumi |
| collection | DOAJ |
| description | Our work is aimed at modeling the American option price by combining the dynamic programming and the optimal stopping time under two asset price models. In doing so, we attempt to control the theoretical error and illustrate the asymptotic characteristics of each model; thus, using a numerical illustration of the convergence of the option price to an equilibrium price, we can notice its behavior when the number of paths tends to be a large number; therefore, we construct a simple estimator on each slice of the number of paths according to an upper and lower bound to control our error. Finally, to highlight our approach, we test it on different asset pricing models, in particular, the exponential Lévy model compared to the simple Black and Scholes model, and we will show how the latter outperforms the former in the real market (Microsoft “MSFT” put option as an example). |
| format | Article |
| id | doaj-art-f7a9a6fff43b4f42a59a1194e5f6d00a |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-f7a9a6fff43b4f42a59a1194e5f6d00a2025-02-03T01:25:12ZengWileyJournal of Applied Mathematics1110-757X1687-00422021-01-01202110.1155/2021/10499071049907An Analysis of Asymptotic Properties and Error Control under the Exponential Jump-Diffusion Model for American Option PricingMohamed Maidoumi0Boubker Daafi1Mehdi Zahid2LAMAI, Cadi Ayyad University, Marrakech, MoroccoLAMAI, Cadi Ayyad University, Marrakech, MoroccoLAMAI, Cadi Ayyad University, Marrakech, MoroccoOur work is aimed at modeling the American option price by combining the dynamic programming and the optimal stopping time under two asset price models. In doing so, we attempt to control the theoretical error and illustrate the asymptotic characteristics of each model; thus, using a numerical illustration of the convergence of the option price to an equilibrium price, we can notice its behavior when the number of paths tends to be a large number; therefore, we construct a simple estimator on each slice of the number of paths according to an upper and lower bound to control our error. Finally, to highlight our approach, we test it on different asset pricing models, in particular, the exponential Lévy model compared to the simple Black and Scholes model, and we will show how the latter outperforms the former in the real market (Microsoft “MSFT” put option as an example).http://dx.doi.org/10.1155/2021/1049907 |
| spellingShingle | Mohamed Maidoumi Boubker Daafi Mehdi Zahid An Analysis of Asymptotic Properties and Error Control under the Exponential Jump-Diffusion Model for American Option Pricing Journal of Applied Mathematics |
| title | An Analysis of Asymptotic Properties and Error Control under the Exponential Jump-Diffusion Model for American Option Pricing |
| title_full | An Analysis of Asymptotic Properties and Error Control under the Exponential Jump-Diffusion Model for American Option Pricing |
| title_fullStr | An Analysis of Asymptotic Properties and Error Control under the Exponential Jump-Diffusion Model for American Option Pricing |
| title_full_unstemmed | An Analysis of Asymptotic Properties and Error Control under the Exponential Jump-Diffusion Model for American Option Pricing |
| title_short | An Analysis of Asymptotic Properties and Error Control under the Exponential Jump-Diffusion Model for American Option Pricing |
| title_sort | analysis of asymptotic properties and error control under the exponential jump diffusion model for american option pricing |
| url | http://dx.doi.org/10.1155/2021/1049907 |
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