The Numerical Solution of Fractional Black-Scholes-Schrodinger Equation Using the RBFs Method

Abstract EN

In this paper, radial basis functions (RBFs) method was used to solve a fractional Black-Scholes-Schrodinger equation in an option pricing of financial problems.

The RBFs method is applied in discretizing a spatial derivative process.

The approximation of time fractional derivative is interpreted in the Caputo’s sense by a simple quadrature formula.

This RBFs approach was theoretically proved with different problems of two numerical examples: time step arbitrage bubble case and time linear arbitrage bubble case.

Then, the numerical results were compared with the semiclassical solution in case of fractional order close to 1.

As a result, both numerical examples showed that the option prices from RBFs method satisfy the semiclassical solution.