Valuation of European call options for the Scott’s stochastic volatility model: An explicit finite difference scheme

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation Pub Date : 2025-04-17 DOI:10.1016/j.matcom.2025.03.033

Freddy H. Marín-Sánchez , Alejandro Pinilla Barrera , Cristhian Montoya Zambrano , Santiago Medina Hurtado

引用次数: 0

Abstract

This paper addresses the construction of an explicit finite difference scheme for options valuation when the underlying asset is described by the stochastic volatility model proposed by Scott (1987). A numerical analysis of the scheme is conducted to ensure positivity, monotonicity, stability, consistency, and convergence conditions. Several numerical experiments are presented for the valuation of European call options, and the results obtained from the explicit finite difference scheme in 2D are compared with Monte Carlo simulations in order to show the feasibility of our results.

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Scott随机波动率模型下欧式看涨期权的估值：一种显式有限差分格式

本文讨论了当标的资产由Scott（1987）提出的随机波动率模型描述时，期权估值的显式有限差分格式的构建。对该方案进行了数值分析，保证了方案的正性、单调性、稳定性、一致性和收敛性。本文对欧式看涨期权的估值进行了数值实验，并将二维显式有限差分格式的结果与蒙特卡罗模拟结果进行了比较，以证明我们的结果的可行性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematics and Computers in Simulation 数学-计算机：跨学科应用

CiteScore

8.90

自引率

4.30%

发文量

335

审稿时长

54 days

期刊介绍： The aim of the journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Published material ranges from short, concise research papers to more general tutorial articles. Mathematics and Computers in Simulation, published monthly, is the official organ of IMACS, the International Association for Mathematics and Computers in Simulation (Formerly AICA). This Association, founded in 1955 and legally incorporated in 1956 is a member of FIACC (the Five International Associations Coordinating Committee), together with IFIP, IFAV, IFORS and IMEKO. Topics covered by the journal include mathematical tools in: •The foundations of systems modelling •Numerical analysis and the development of algorithms for simulation They also include considerations about computer hardware for simulation and about special software and compilers. The journal also publishes articles concerned with specific applications of modelling and simulation in science and engineering, with relevant applied mathematics, the general philosophy of systems simulation, and their impact on disciplinary and interdisciplinary research. The journal includes a Book Review section -- and a "News on IMACS" section that contains a Calendar of future Conferences/Events and other information about the Association.