Investigation of convergence analysis of the stochastic Heston model with one singular point

Shandal Hashim, Ali; Najafi, Esmaeil; Ahmadian, Davood; Farkhonde Rouz, Omid

doi:10.22034/cmde.2025.64394.2921

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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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Investigation of convergence analysis of the stochastic Heston model with one singular point