# A weighted finite difference method for subdiffusive Black Scholes Model

## TL;DR

This paper develops a weighted finite difference numerical method for the subdiffusive Black-Scholes model, providing stability, convergence analysis, and demonstrating its effectiveness through numerical results.

## Contribution

It introduces a generalized weighted finite difference scheme for the subdiffusive Black-Scholes equation with proven stability and convergence properties.

## Key findings

- The method achieves $2-eta$ order accuracy in time.
- The scheme is unconditionally stable.
- Numerical tests confirm the theoretical convergence rates.

## Abstract

In this paper we focus on the subdiffusive Black Scholes model. The main part of our work consists of the finite difference method as a numerical approach to the option pricing in the considered model. We derive the governing fractional differential equation and the related weighted numerical scheme being a generalization of the classical Crank-Nicolson scheme. The proposed method has $2-\alpha$ order of accuracy with respect to time where $\alpha\in(0,1)$ is the subdiffusion parameter, and $2$ with respect to space. Further, we provide the stability and convergence analysis. Finally, we present some numerical results.