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Investigation of convergence analysis of the stochastic Heston model with one singular point | ||
| Computational Methods for Differential Equations | ||
| مقاله 5، دوره 14، شماره 1، فروردین 2026، صفحه 50-59 اصل مقاله (403.91 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.64394.2921 | ||
| نویسندگان | ||
| Ali Shandal Hashim1؛ Esmaeil Najafi1؛ Davood Ahmadian* 2؛ Omid Farkhonde Rouz2 | ||
| 1Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran. | ||
| 2Faculty of Mathematics, Statistics and Computer Sciences, University of Tabriz, Tabriz, Iran. | ||
| چکیده | ||
| The Heston model is a popular stochastic volatility model used in financial mathematics for option pricing. This paper focuses on the stochastic Heston model (SHM) with one singular point. In this way, we first consider the existence, uniqueness, and boundedness of the numerical solution under the global Lipschitz condition and the linear growth condition. In addition, the stochastic ${\theta}$-scheme is developed to solve the equation numerically, and we obtain a convergence rate with $\min \{2-2\alpha, 1-2\beta \}$ which depends on the kernel parameters. Moreover, Monte Carlo (M.C.) simulation is implemented for this kind of problem in the 95 percent confidence interval, which reveals that it verifies the stochastic ${\theta}$-scheme results. Finally, a numerical example is given to show the validity and effectiveness of the theoretical results. | ||
| کلیدواژهها | ||
| Stochastic Heston model؛ Singular point؛ Convergence analysis؛ Existence and uniqueness؛ Option pricing؛ Monte Carlo simulation | ||
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آمار تعداد مشاهده مقاله: 142 تعداد دریافت فایل اصل مقاله: 207 |
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