Numerical solution of stochastic models using spectral collocation method

Abdous, Mehrnosh; Vahidi, Alireza; Damercheli, Tayebeh

doi:10.22034/cmde.2023.54948.2284

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	Numerical solution of stochastic models using spectral collocation method
Computational Methods for Differential Equations
مقاله 14، دوره 11، شماره 3، شهریور 2023، صفحه 630-642 اصل مقاله (328.54 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.54948.2284
نویسندگان
Mehrnosh Abdous؛ Alireza Vahidi ؛ Tayebeh Damercheli
Department of Mathematics, Yadegar-e-Imam khomeini (RAH) Share Rey Branch, Islamic Azad University, Tehran, Iran.
چکیده
In this article, the spectral collocation method based on radial basis functions is used to solve the mentioned models. The advantage of this method is that it converts the equations into a system of algebraic equations. Therefore, we can solve this problem with Newton's method. The purpose of this article is to numerically solve stochastic models such as the Heston model, Vasicek model, Cox-Ingersoll and Ross model, and a model of the Black-Scholes called the Genral Stock model. The method is computationally attractive, and numerical examples confirm the validity and efficiency of the proposed method.
کلیدواژه‌ها
Vasicek Model؛ Cox-Ingersoll and Ross model؛ Genral stock model؛ the P panels M-point NewtonCotes rules؛ The spectral collocation method based on radial basis functions

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Numerical solution of stochastic models using spectral collocation method