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A Dynamic Hybrid Option Pricing Model by Genetic Algorithm and Black Scholes Model
"... Abstract—Unlike this study focused extensively on trading behavior of option market, those researches were just taken their attention to modeldriven option pricing. For example, BlackScholes (BS) model is one of the most famous option pricing models. However, the arguments of BS model are previo ..."
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Abstract—Unlike this study focused extensively on trading behavior of option market, those researches were just taken their attention to modeldriven option pricing. For example, BlackScholes (BS) model is one of the most famous option pricing models. However, the arguments of BS model are previously mentioned by some pricing models reviewing. This paper following suggests the importance of the dynamic character for option pricing, which is also the reason why using the genetic algorithm (GA). Because of its natural selection and species evolution, this study proposed a hybrid model, the GeneticBS model which combining GA and BS to estimate the price more accurate. As for the final experiments, the result shows that the output estimated price with lower MAE value than the calculated price by either BS model or its enhanced one, GramCharlier garch (GC garch) model. Finally, this work would conclude that the GeneticBS pricing model is exactly practical. Keywords—genetic algorithm, GeneticBS, option pricing model. I.
A highorder compact method for nonlinear BlackScholes option pricing equations of American Options A highorder compact method for nonlinear BlackScholes option pricing equations of American Options
"... Due to transaction costs, illiquid markets, large investors or risks from an unprotected portfolio the assumptions in the classical BlackScholes model become unrealistic and the model results in nonlinear, possibly degenerate, parabolic diffusionconvection equations. Since in general, a closedfo ..."
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Due to transaction costs, illiquid markets, large investors or risks from an unprotected portfolio the assumptions in the classical BlackScholes model become unrealistic and the model results in nonlinear, possibly degenerate, parabolic diffusionconvection equations. Since in general, a closedform solution to the nonlinear BlackScholes equation for American options does not exist (even in the linear case), these problems have to be solved numerically. We present from the literature different compact finite difference schemes to solve nonlinear BlackScholes equations for American options with a nonlinear volatility function. As compact schemes cannot be directly applied to American type options, we use a fixed domain transformation proposed byŠevčovič and show how the accuracy of the method can be increased to order four in space and time.
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"... 2. L. Acedo, Training of an attractor neural network in a stochastic environment.. Pag: 915 ..."
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2. L. Acedo, Training of an attractor neural network in a stochastic environment.. Pag: 915
Research Article An Unconditionally Stable, PositivityPreserving Splitting Scheme for Nonlinear BlackScholes Equation with Transaction Costs
"... Copyright © 2014 J. Guo and W. Wang.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper deals with the numerical analysis of n ..."
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Copyright © 2014 J. Guo and W. Wang.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper deals with the numerical analysis of nonlinear BlackScholes equation with transaction costs. An unconditionally stable and monotone splitting method, ensuring positive numerical solution and avoiding unstable oscillations, is proposed. This numerical method is based on the LODBackward Euler method which allows us to solve the discrete equation explicitly. The numerical results for vanilla call option and for European butterfly spread are provided. It turns out that the proposed scheme is efficient and reliable. 1.