Mathematical Modeling of Stock Price Behavior and Option Valuation

• Published in: Mathematics and Modeling in Finance Vol. 1; no. 1; pp. 159 - 178
• Main Author: Moslem Peymany
• Format: Journal Article
• Language: English
• Published: Allameh Tabataba'i University Press 01.03.2021
• Subjects: finite difference; monte carlo simulation; options; stochastic differential equations; stocks
• ISSN: 2783-0578; 2783-056X
• DOI: 10.22054/jmmf.2020.56846.1022

This study emphasizes on the mathematical modeling procedure of stock price behavior and option valuation in order to highlight the role and importance of advanced mathematics and subsequently computer software in financial analysis. To this end, following price process modeling and explaining the procedure of option pricing based on it, the resulting model is solved using advanced numerical methods and is executed by MATLAB software. As derivatives pricing models are based on price behavior of underling assets and are subject to change as a result of variation in the behavior of the asset, studying the price behavior of underlying asset is of significant importance. A number of such models (such as Geometric Brownian Motion and jump-diffusion model) are, therefore, analyzed in this article, and results of their execution based on real data from Tehran Stock Exchange total index are presented by parameter estimation and simulation methods and also by using numerical methods.