Liquidity is an overlooked research area, yet it plays a crucial role in financial markets. Trading system developers often use the bid-ask spread as a proxy for liquidity, but this approach is less effective in the options market.
Reference [1] proposes a method for integrating liquidity into the option pricing model. Essentially, it introduces market liquidity as a variable that can change randomly and affects stock prices through a discounting factor and market liquidity levels.
The paper begins by incorporating a stochastic liquidity variable into the SDE for stock price under the P measure. Here the liquidity process is modeled as an Ornstein-Uhlenbeck process. The SDE is then transformed into the Q measure in which European options are analytically evaluated using the derived closed-form characteristic function. The authors pointed out,
We incorporate three main factors, that is, stochastic volatility, economic cycles, and liquidity risks, into one model used for option pricing. A combination of Heston stochastic volatility and regime switching is selected for modeling the price of the underlying stock when there are no liquidity risks. The stock price is then discounted based on the level of market liquidity levels described by a mean reverting stochastic process. The employment of regime switching Esscher transform provides a risk‐neutral measure as well as the corresponding model dynamics, yielding a European option pricing formula in closed form. Significant impacts of the three factors can be seen through the performed numerical experiments. Our analysis with real data also confirm the necessity to consider stochastic liquidity, which has greatly improved model performance. By leveraging the stochastic liquidity component, our proposed model can help investors refine their hedging positions, better responding to liquidity shocks, and thus mitigate risks more effectively.
In short, liquidity is integrated as a discount factor, and the study demonstrates its impact on option prices.
This research provides a framework for incorporating liquidity into options trading, however, we found it less intuitive. Let us know what you think in the comments below or in the discussion forum.
References
[1] Xin-Jiang He, Hang Chen, Sha Lin, A Closed-Form Formula for Pricing European Options With Stochastic Volatility, Regime Switching, and Stochastic Market Liquidity, Journal of Futures Markets, 2025; 1–12
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