带学习参数的自适应微分进化障碍期权定价近似解

Mendel Pub Date : 2022-12-20 DOI:10.13164/mendel.2022.2.076
Werry Febrianti, K. A. Sidarto, N. Sumarti
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引用次数: 1

摘要

布莱克-斯科尔斯(Black-Scholes, BS)方程是以随机偏微分方程的形式出现的,是数学金融学尤其是期权定价中的基本方程。尽管存在标准形式的解析解,但这些方程的数值解并不简单。这种有效的数值方法将为今后求解高级和非标准形式的BS方程提供参考。在本文中,我们提出了一种用优化问题的方法来求解BS方程的方法,其中使用元启发式优化算法来寻找方程的最优逼近解。在这里,我们使用带有学习参数的自适应差分进化(ADELP)算法。所求解的BS方程旨在求出具有障碍期权定价的欧式期权定价的值。我们的近似方法的结果与解析近似解吻合得很好。
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Approximate Solution for Barrier Option Pricing Using Adaptive Differential Evolution With Learning Parameter
Black-Scholes (BS) equations, which are in the form of stochastic partial differential equations, are fundamental equations in mathematical finance, especially in option pricing. Even though there exists an analytical solution to the standard form, the equations are not straightforward to be solved numerically. The effective and efficient numerical method will be useful to solve advanced and non-standard forms of BS equations in the future. In this paper, we propose a method to solve BS equations using an approach of optimization problems, where a metaheuristic optimization algorithm is utilized to find the best-approximated solutions of the equations. Here we use the Adaptive Differential Evolution with Learning Parameter (ADELP) algorithm. The BS equations being solved are meant to find values of European option pricing that is equipped with Barrier option pricing. The result of our approximation method fits well to the analytical approximation solutions.
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来源期刊
Mendel
Mendel Decision Sciences-Decision Sciences (miscellaneous)
CiteScore
2.20
自引率
0.00%
发文量
7
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