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Approximate solution of fractional Black-Scholes European option pricing equation by using ETHPM. (Approximate solution of fractional Black-Schole’s European option pricing equation by using ETHPM.) (English) Zbl 1453.91106

Summary: We proposed a new reliable combination of new Homotopy Perturbation Method (HPM) and Elzaki transform called as Elzaki Transform Homotopy Perturbation Method (ETHPM) is designed to obtain a exact solution to the fractional Black-Scholes equation with boundary condition for a European option pricing problem. The fractional derivative is in Caputo sense and the nonlinear terms in Fractional Black-Scholes Equation can be handled by using HPM. 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 methods give an analytic solution of the fractional Black-Scholes equation in the form of a convergent series. Finally, some examples are included to demonstrate the validity and applicability of the proposed technique.

MSC:

91G60 Numerical methods (including Monte Carlo methods)
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65R10 Numerical methods for integral transforms
35R11 Fractional partial differential equations
91G20 Derivative securities (option pricing, hedging, etc.)
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