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Selection of shape parameter in radial basis functions for solution of time-fractional Black–Scholes models

Sirajul Haq and Manzoor Hussain

Applied Mathematics and Computation, 2018, vol. 335, issue C, 248-263

Abstract: The current work aims to exploit two techniques namely: Residual Power Series method (RPSM) and collocation based meshfree method, for the solution of time-fractional Black–Scholes models with constant and variable coefficients. Firstly, using RPSM, we obtain exact solutions of the considered models and then numerical solution by meshfree method. Computer simulations are performed for three test problems of European options pricing. The simulations features excellent agreement with exact solutions. Accuracy and efficiency of the proposed numerical method is assessed via E2, E∞ and Erms error norms. Convergence of the proposed methods is also analyzed.

Keywords: Residual Power Series method; Meshfree method; Radial basis function; Black–Scholes equation; Caputo fractional derivative (search for similar items in EconPapers)
Date: 2018
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Handle: RePEc:eee:apmaco:v:335:y:2018:i:c:p:248-263