Analytically Pricing European Options Under Two‐Factor Stochastic Volatility With Stochastic Liquidity Risks

ABSTRACT This article examines the pricing of European options while incorporating liquidity risks, extending the classical Heston stochastic volatility framework. A new methodology is proposed by incorporating both liquidity risk and stochastic long‐term variance into the model, improving its capacity to reflect market dynamics. By applying measure transformation, the model dynamics are formulated under an equivalent martingale measure, leading to an analytical expression for the characteristic function of the stock price logarithm. This yields a closed‐form solution for European option pricing, which is subsequently benchmarked against existing models through numerical simulations to evaluate its pricing accuracy and parameter sensitivity. Empirical analysis is conducted to examine the performance of the model using market data.