In this research we have considered the European option pricing and its Greeks in high volatile illiquid market. Since the classic Black-Scholes model has been formulated on a complete market without any illiquidity, transaction cost and large investor performance, recently several nonlinear Black-Scholes modes have been introduced to take one or more of these parameters into account to achieve more accurate the option prices. Here we investigated the finite difference schemes to obtain the call option pricing and its Greeks in an illiquid market with financial crisis and compare it with an illiquid market without high volatility and also the call option in the classic liquid market.
