This study compares the performance of the classic Black-Scholes model and the generalized Liu and Young model in pricing European options and calculating derivatives sensitivities in high volatile illiquid markets. The generalized Liu and Young model is a more accurate option pricing model that incorporates both the efficacy of the number of invested stocks and the abnormal increase of volatility during a financial crisis for hedging purposes and the financial risk management. To evaluate the performance of these models, we use numerical methods such as finite difference schemes and Monte-Carlo simulation with antithetic variate variance reduction technique. Our results show that the generalized Liu and Young model outperforms the classic Black-Scholes model in terms of accuracy, especially in high volatile illiquid markets. Additionally, we find that the finite difference schemes are more efficient and faster than the Monte-Carlo simulation in this model. Based on these findings, we recommend using the generalized Liu and Young model with finite difference schemes for the European options and Greeks valuing in high volatile illiquid markets.
