关于布莱克-斯科尔斯美式看涨期权模型

IF 1.9 4区经济学 Q2 ECONOMICS

Computational Economics Pub Date : 2024-05-25 DOI:10.1007/s10614-024-10623-3

Morteza Garshasbi, Shadi Malek Bagomghaleh

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引用次数: 0

摘要

本研究将 Black-Scholes 美式看涨期权模型视为移动边界问题。利用前固定方法，将该模型推导为一个定域非线性抛物线问题，并确定了看涨期权价格和临界股票价格的唯一性。建立了数值求解该问题的迭代法，并证明了迭代法的收敛性。在计算实现方面，采用了有限差分方案和二阶 Runge-Kutta 方法。最后，报告了两个测试问题的数值结果，以证实我们的理论成果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

On a Black–Scholes American Call Option Model

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On a Black–Scholes American Call Option Model

This study focuses on the Black–Scholes American call option model as a moving boundary problem. Using a front-fixing approach, the model is derived as a fixed domain nonlinear parabolic problem, and the uniqueness of both the call option price and critical stock price is established. An iterative approach is established to numerically solve the problem, and the convergence of the iterative method is proved. For computational implementation, a finite difference scheme in conjunction with a second-order Runge–Kutta method is conducted. Finally, the numerical results for two test problems are reported in order to confirm our theoretical achievements.

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来源期刊

Computational Economics MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

4.00

自引率

15.00%

发文量

119

审稿时长

12 months

期刊介绍： Computational Economics, the official journal of the Society for Computational Economics, presents new research in a rapidly growing multidisciplinary field that uses advanced computing capabilities to understand and solve complex problems from all branches in economics. The topics of Computational Economics include computational methods in econometrics like filtering, bayesian and non-parametric approaches, markov processes and monte carlo simulation; agent based methods, machine learning, evolutionary algorithms, (neural) network modeling; computational aspects of dynamic systems, optimization, optimal control, games, equilibrium modeling; hardware and software developments, modeling languages, interfaces, symbolic processing, distributed and parallel processing