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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Brno University of Technology
2022-12-01
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| Series: | Mendel |
| Subjects: | |
| Online Access: | http://46.28.109.63/index.php/mendel/article/view/194 |
| _version_ | 1811293210073366528 |
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| author | Werry Febrianti Kuntjoro Adji Sidarto Novriana Sumarti |
| author_facet | Werry Febrianti Kuntjoro Adji Sidarto Novriana Sumarti |
| author_sort | Werry Febrianti |
| collection | DOAJ |
| description |
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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| first_indexed | 2024-04-13T04:57:06Z |
| format | Article |
| id | doaj.art-7ccec895fc0b49c2bb371baeb488c612 |
| institution | Directory Open Access Journal |
| issn | 1803-3814 2571-3701 |
| language | English |
| last_indexed | 2024-04-13T04:57:06Z |
| publishDate | 2022-12-01 |
| publisher | Brno University of Technology |
| record_format | Article |
| series | Mendel |
| spelling | doaj.art-7ccec895fc0b49c2bb371baeb488c6122022-12-22T03:01:26ZengBrno University of TechnologyMendel1803-38142571-37012022-12-0128210.13164/mendel.2022.2.076Approximate Solution for Barrier Option Pricing Using Adaptive Differential Evolution With Learning ParameterWerry Febrianti0Kuntjoro Adji Sidarto1Novriana Sumarti2Departmen Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi BandungDepartmen Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi BandungDepartmen Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung 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. http://46.28.109.63/index.php/mendel/article/view/194Adaptive differential evolutionApproximation solutionBlack-ScholesMetaheuristic optimizationPartial differential equations |
| spellingShingle | Werry Febrianti Kuntjoro Adji Sidarto Novriana Sumarti Approximate Solution for Barrier Option Pricing Using Adaptive Differential Evolution With Learning Parameter Mendel Adaptive differential evolution Approximation solution Black-Scholes Metaheuristic optimization Partial differential equations |
| title | Approximate Solution for Barrier Option Pricing Using Adaptive Differential Evolution With Learning Parameter |
| title_full | Approximate Solution for Barrier Option Pricing Using Adaptive Differential Evolution With Learning Parameter |
| title_fullStr | Approximate Solution for Barrier Option Pricing Using Adaptive Differential Evolution With Learning Parameter |
| title_full_unstemmed | Approximate Solution for Barrier Option Pricing Using Adaptive Differential Evolution With Learning Parameter |
| title_short | Approximate Solution for Barrier Option Pricing Using Adaptive Differential Evolution With Learning Parameter |
| title_sort | approximate solution for barrier option pricing using adaptive differential evolution with learning parameter |
| topic | Adaptive differential evolution Approximation solution Black-Scholes Metaheuristic optimization Partial differential equations |
| url | http://46.28.109.63/index.php/mendel/article/view/194 |
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