A stochastic liquidity risk model with stochastic volatility and its applications to option pricing

We investigate the pricing problem of European options when the underlying stock is associated with liquidity risks. Under our established framework, stock prices are assumed to follow the Heston stochastic volatility model when liquidity risks can be ignored, and liquidity risks arise from stochastic market liquidity, which influences stock prices based on a liquidity discounting factor. Through measure transformation, we first obtain model dynamics under an equivalent martingale measure, and work out the corresponding characteristic function associated with the logarithm of stock prices analytically. This yields the option price formulation in closed form. Finally, we compare numerically the performance of our model and that of some relevant models, and parameter sensitivity is also discussed.