Abstract
In this paper, we investigate the numerical valuation of European and American options under the time fractional Black-Scholes model. We first apply a coordinate stretching transformation to the asset price so that the spatial region can focus on the vicinity of singularities, which are usually found in the payoff function. The radial basis function finite difference method is used for the spatial discretization, and the improved L1 method is used to deal with the reduced order of convergence for the nonsmooth initial data. We use the operator splitting method for solving the linear complementary problem of American options. The proposed scheme leads to a sparse linear system which is trivial to solve. Moreover, the stability of the proposed numerical scheme is analyzed using Fourier analysis. Numerical experiments demonstrate the accuracy and efficiency of the proposed method.
Highlights
Golbabai et al [26] developed a numerical method, using the meshless method based on the radial basis function (RBF) collocation method for European options under the Wyss time fractional B-S model
We propose a new combination of the radial basis function finite difference (RBF-FD) and the improved L1 operator splitting methods for American options, inspired by [27,30,31]
We investigate the numerical valuation of European and American options under the time fractional Black-Scholes model
Summary
Song and Wang [22] used an implicit finite difference method for European and American put options under the Jumarie time fractional B-S model. Zhang et al [23] constructed an implicit numerical scheme using the finite difference method for European options under the Wyss time fractional B-S model. Golbabai et al [26] developed a numerical method, using the meshless method based on the radial basis function (RBF) collocation method for European options under the Wyss time fractional B-S model. Proposed the improved L1 operator splitting and spectral methods for American options under the time-space fractional B-S model. We propose a new combination of the radial basis function finite difference (RBF-FD) and the improved L1 operator splitting methods for American options, inspired by [27,30,31].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
