Numerical Simulations for Time-Fractional Black-Scholes Equations

TL;DR

This paper introduces an efficient, unconditionally stable numerical method combining Crank-Nicolson and exponential B-splines for solving time-fractional Black-Scholes equations, validated through numerical examples.

Contribution

It presents a novel numerical algorithm that improves stability and accuracy for time-fractional Black-Scholes models using combined discretization techniques.

Findings

The method is unconditionally stable.

Numerical examples confirm the accuracy.

Proposed approach outperforms existing methods.

Abstract

This paper implements an efficient numerical algorithm for the time-fractional Black-Scholes model governing European options. The proposed method comprises the Crank-Nicolson approach to discretize the time variable and exponential B-spline approximation for the space variable. The implemented method is unconditionally stable. We present few numerical examples to confirm the theory. Numerical simulations with comparisons exhibit the supremacy of the proposed approach.