First Hitting Time and Option Pricing Problem Under Geometric Brownian Motion with Singular Volatility

Q3 Mathematics

WSEAS Transactions on Mathematics Pub Date : 2023-11-22 DOI:10.37394/23206.2023.22.95

Haoyan Zhang, Yece Zhou, Xuan Li, Yinyin Wu

引用次数: 0

Abstract

In this paper, we discuss the first hitting time and option pricing problem under Geometric Brownian motion with singular volatility. By solving the Sturm-Liouville equation and introducing probability scheme, we derive the closed-form solutions to the target problems. At last, numerical results are provided to analyze our calculations.

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几何布朗运动与奇异波动下的首次击球时间和期权定价问题

本文讨论了具有奇异波动率的几何布朗运动下的首次击球时间和期权定价问题。通过求解 Sturm-Liouville 方程和引入概率方案，我们得出了目标问题的闭式解。最后，我们提供了数值结果来分析我们的计算。

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

WSEAS Transactions on Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： WSEAS Transactions on Mathematics publishes original research papers relating to applied and theoretical mathematics. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with linear algebra, numerical analysis, differential equations, statistics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.