Pseudospectral methods for option pricing problems modeling of illiquid markets

Pseudospectral methods for option pricing problems modeling of illiquid markets

In this paper, we study the numerical solutions of nonlinear BlackScholes equations modeling illiquid markets where the implementation of a dynamic hedging strategy affects the price process of the underlying asset. Then, we present two pseudospectral methods based on Fourier series and rational Chebyshev functions for solving this Equation. With tasing this mEthods, we can decrease partial differential equation to an ordinary differential equations that is solved by the leapfrog difference scheme and the fourthoreder Runge-Kutta, method, respectively