A Closed-Form Formula for Pricing European Options With Stochastic Volatility, Regime Switching, and Stochastic Market Liquidity

Abstract

We consider European option pricing when the volatility of the underlying stock is stochastic and affected by economic cycles. We further assume that market liquidity risks have a significant impact on the price of the stock that is not negligible, and stock prices should be adjusted according to a liquidity discounting factor. For the purpose of option pricing, we transform the established model dynamics under the physical measure into those under a risk-neutral measure, which forms a foundation in the subsequent closed-form derivation of the characteristic function. An analytical option pricing formula is then obtained, and numerical tests together with sensitivity analysis are also performed. Through an empirical analysis, we demonstrate that our model, which incorporates stochastic liquidity, significantly outperforms the version with constant liquidity.