Numerical Valuation of Time Fractional Black–Scholes Equation in Financial Markets
Omid Nikan, Mehdi Alaeiyan, Suhad Yousef
Source abstract
The time-fractional Black–Scholes model (TFBSM) is used to describe option price dynamics within a fractional diffusion model. It provides a mathematical model for valuing European and American call and put options on non-dividend-paying stocks. In this paper, the TFBSM is solved numerically for European and American option pricing using a local meshless interpolation approach. The time-fractional derivative is approximated by a finite difference scheme with accuracy of order 2−α for 0<α<1, while the spatial derivatives are discretized using the local radial point interpolation method (LRPIM). Theoretical analysis establishes the unconditional stability and convergence of the time-semi-discrete scheme in the L2 norm. Numerical examples are presented to confirm the theoretical results and demonstrate the accuracy and performance of the proposed method for fractional option pricing problems.
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