Option pricing in high volatile illiquid market

Abstract

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 pur- poses 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 tech- nique. Our results show that the generalized Liu and Young model outper- forms the classic Black-Scholes model in terms of accuracy, especially in high volatile illiquid markets. Additionally, we find that the finite differ- ence schemes are more efficient and faster than the Monte-Carlo simulation in this model. Based on these findings, we recommend using the general- ized Liu and Young model with finite difference schemes for the European options and Greeks valuing in high volatile illiquid markets.

Keywords

• black-scholes equation
• finite difference scheme
• greeks
• monte-carlo simulation
• nonlinear partial differential equation