# A 2nd-Order FDM for a 2D Fractional Black-Scholes Equation

• W. Chen
• S. Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10187)

## Abstract

We develop a finite difference method (FDM) for a 2D fractional Black-Scholes equation arising in the optimal control problem of pricing European options on two assets under two independent geometric Lévy processes. We establish the convergence of the method by showing that the FDM is consistent, stable and monotone. We also show that the truncation error of the FDM is of 2nd order. Numerical experiments demonstrate that the method produces financially meaningful results when used for solving practical problems.

## Keywords

Fractional Derivative Option Price Truncation Error Finite Difference Method Underlying Asset
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Notes

### Acknowledgements

S. Wang’s work was partially supported by the AOARD Project #15IOA095.

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