2022
DOI: 10.13164/mendel.2022.2.076
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Approximate Solution for Barrier Option Pricing Using Adaptive Differential Evolution With Learning Parameter

Abstract: 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 appr… Show more

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Cited by 3 publications
(3 citation statements)
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“…Although there has been an explosion of "novel" evolutionary methods that draw on these principles [38][39][40], many of which were found to hide their lack of novelty behind a flawed experimental analysis [41][42][43][44] or a metaphor-rich jargon [45,46], these techniques are still among the most-utilized methods for diverse and complex applications, where the use of standard optimization methods is either found to be inadequate or overly computationally demanding [47,48]. Among these applications are for instance the design of mechanical components [49], quantum operators [50] or airfoil geometry [51], landslide displacement prediction [52], inverse kinematics control of a robot [53], or barrier option pricing in economics [54].…”
Section: Evolutionary Algorithmsmentioning
confidence: 99%
“…Although there has been an explosion of "novel" evolutionary methods that draw on these principles [38][39][40], many of which were found to hide their lack of novelty behind a flawed experimental analysis [41][42][43][44] or a metaphor-rich jargon [45,46], these techniques are still among the most-utilized methods for diverse and complex applications, where the use of standard optimization methods is either found to be inadequate or overly computationally demanding [47,48]. Among these applications are for instance the design of mechanical components [49], quantum operators [50] or airfoil geometry [51], landslide displacement prediction [52], inverse kinematics control of a robot [53], or barrier option pricing in economics [54].…”
Section: Evolutionary Algorithmsmentioning
confidence: 99%
“…Although options and structured warrants are quite different, the pricing method could be similar due to their properties. Some research about option pricing using adaptive differential evolution and option portfolio construction are [7] and [20].…”
Section: Introductionmentioning
confidence: 99%
“…Among them are classical techniques such as the genetic algorithm (GA), the evolutionary strategy (ES), differential evolution (DE), or particle swarm optimization (PSO). Many of these methods found their use in diverse and complex applications, where the utilization of exact optimization algorithms was either found to be inadequate or computationally too expensive [9], such as the design of mechanical components [10] and quantum operators [11], feature selection [12,13], landslide displacement prediction [14], airfoil geometry design [15], or barrier option pricing in economics [16]. Another class of methods that is popular for such complex optimization problems is the class of the deterministic DIRECT (which is an acronym of DIviding RECTangles) algorithms [17].…”
Section: Introductionmentioning
confidence: 99%