The aim of this paper is to numerically price the European double barrier option by calculating the governing fractional Black-Scholes equation in illiquid markets. Incorporating the price impact into the underlying asset dynamic, which means that trading strategies affect the underlying price, we consider markets with - nite liquidity. We survey both cases of rst-order feedback and full feedback. Asset evolution satis es a stochastic differential equation with fractional noise, which is more realistic in markets with statistical dependence. Moreover, the Sinc- collocation method is used to price the option. Numerical experiments show that the results highly correspond to our expectation of illiquid markets.
