Analytical Solution of Fractional Black-scholes European Option Pricing Equation by Using Laplace Transform
نویسنده
چکیده
In this paper, Laplace homotopy perturbation method, which is combined form of the Laplace transform and the homotopy perturbation method, is employed to obtain a quick and accurate solution to the fractional Black Scholes equation with boundary condition for a European option pricing problem. The Black-Scholes formula is used as a model for valuing European or American call and put options on a non-dividend paying stock. The proposed scheme finds the solutions without any discretization or restrictive assumptions and is free from round-off errors and therefore, reduces the numerical computations to a great extent. The analytical solution of the fractional Black Scholes equation is calculated in the form of a convergent power series with easily computable components. Two examples are presented.
منابع مشابه
European option pricing of fractional Black-Scholes model with new Lagrange multipliers
In this paper, a new identification of the Lagrange multipliers by means of the Sumudu transform, is employed to btain a quick and accurate solution to the fractional Black-Scholes equation with the initial condition for a European option pricing problem. Undoubtedly this model is the most well known model for pricing financial derivatives. The fractional derivatives is described in Caputo sen...
متن کاملBarrier options pricing of fractional version of the Black-Scholes model
In this paper two different methods are presented to approximate the solution of the fractional Black-Scholes equation for valuation of barrier option. Also, the two schemes need less computational work in comparison with the traditional methods. In this work, we propose a new generalization of the two-dimensional differential transform method and decomposition method that will extend the appli...
متن کاملNumerical Solutions for Fractional Black-Scholes Option Pricing Equation
In this article we have applied a numerical finite difference method to solve the Black-Scholes European and American option pricing both presented by fractional differential equations in time and asset.
متن کاملA new approach to using the cubic B-spline functions to solve the Black-Scholes equation
Nowadays, options are common financial derivatives. For this reason, by increase of applications for these financial derivatives, the problem of options pricing is one of the most important economic issues. With the development of stochastic models, the need for randomly computational methods caused the generation of a new field called financial engineering. In the financial engineering the pre...
متن کاملBarrier options pricing of fractional version of the Black-Scholes model
In this paper two different methods are presented to approximate the solution of the fractional BlackScholes equation for valuation of barrier option. Also, the two schemes need less computational work in comparison with the traditional methods. In this work, we propose a new generalization of the two-dimensional differential transform method and decomposition method that will extend the applic...
متن کامل