TY - JOUR AU - Werry Febrianti AU - Kuntjoro Sidarto AU - Novriana Sumarti PY - 2022/12/20 Y2 - 2024/03/29 TI - Approximate Solution for Barrier Option Pricing Using Adaptive Differential Evolution With Learning Parameter JF - MENDEL JA - mendel VL - 28 IS - 2 SE - Research articles DO - 10.13164/mendel.2022.2.076 UR - https://mendel-journal.org/index.php/mendel/article/view/194 AB - 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. ER -