Option Pricing Model in Illiquid Markets

Key Takeaways

• Liquidity discount factor modifies Black‑Scholes valuation
• Mean‑reverting process models market‑wide liquidity dynamics
• Closed‑form solution enables fast, accurate pricing
• Volatility haircut approximates liquidity risk in practice
• Model improves hedging strategies for illiquid assets

Summary

The 2022 study by Pasricha, Zhu, and He extends the Black‑Scholes‑Merton framework by introducing a liquidity discount factor that reflects market‑wide illiquidity. Using a mean‑reverting stochastic process for liquidity, the authors derive a closed‑form pricing formula for European options. Numerical tests confirm the formula’s accuracy and highlight the material price impact of liquidity risk. The work formally links the industry‑used volatility haircut to an underlying liquidity adjustment mechanism.

Pulse Analysis

The Black‑Scholes‑Merton (BSM) model has long been the cornerstone of European option pricing, prized for its analytical tractability and clear assumptions about constant volatility and perfect market liquidity. In practice, however, many underlying assets exhibit thin trading, wide bid‑ask spreads, and price impact that BSM ignores. This disconnect has prompted researchers to explore stochastic volatility extensions, yet few have tackled the liquidity dimension head‑on, leaving a gap in both academic literature and real‑world pricing tools.

Pasricha, Zhu, and He address this gap by modeling market‑wide liquidity as a mean‑reverting stochastic process, effectively treating liquidity as a state variable that influences the underlying asset’s dynamics. Leveraging the Feynman–Kac theorem, they derive a closed‑form pricing formula that incorporates a liquidity discount factor, allowing practitioners to compute option values without resorting to costly Monte‑Carlo simulations. Their numerical experiments demonstrate that ignoring liquidity can misprice options by several percentage points, underscoring the practical relevance of the model for traders dealing with illiquid equities, corporate bonds, or exotic derivatives.

The introduction of a formal liquidity adjustment has immediate implications for risk management and regulatory compliance. By quantifying liquidity risk, firms can refine hedging strategies, adjust margin requirements, and better align capital reserves with actual market conditions. Moreover, the study bridges the heuristic "volatility haircut"—a common industry practice—to a theoretically grounded framework, offering a pathway for integrating the new model into existing pricing systems. As markets evolve and liquidity becomes an increasingly volatile factor, such models are poised to become essential components of sophisticated trading desks and quantitative research labs.