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

Abstract

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.

Keywords:

• Analytical formula
• characteristic function
• option pricing
• stochastic liquidity
• stochastic volatility

Acknowledgments

The authors would like to gratefully acknowledge the anonymous referees’ constructive comments and suggestions, which greatly help to improve the completeness and readability of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (No. 12301614, No. 12101554), the Research Funds for Tailong Finance School of Zhejiang Gongshang University (No. TFS23KY010), and the Fundamental Research Funds for Zhejiang Provincial Universities (No. GB202103001).