Asset Pricing in the Presence of Market Microstructure Noise

2025-10-31

AI Summary

This paper investigates the impact of market microstructure noise on the dynamic pricing of assets and European options. Addressing the limitation of existing models—which neglect the dual perturbation of noise on both drift and volatility—we propose two novel frameworks: (i) a continuous-time Black–Scholes–Merton model augmented with noise-corrected dynamic risk-neutral measures, and (ii) an extension of the Grossman–Stiglitz static framework into the first dynamic discrete binomial tree model capable of jointly capturing noise-induced distortions in drift and volatility. Methodologically, we integrate equivalent martingale measure transformations, high-frequency data-driven parameter estimation, and noise separation techniques. Empirically, our models uniquely identify noise parameters and significantly improve in-sample and out-of-sample fit of price dynamics under high-frequency observation. The results provide both theoretical foundations and implementable tools for option pricing and risk management in noisy market environments.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Advertising auctions, pricing, markets, and exchanges
• Security and Privacy: Large-scale security measurements

Abstract

We present two models for incorporating the total effect of market microstructure noise into dynamic pricing of assets and European options. The first model is developed under a Black-Scholes-Merton, continuous-time framework. The second model is a discrete, binomial tree model developed as an extension of the static Grossman-Stiglitz model. Both models are market complete, providing a unique equivalent martingale measure that establishes a unique map between parameters governing the risk-neutral and real-world price dynamics. We provide empirical examples to extract the coefficients in the model, in particular those coefficients characterizing the influence of the microstructure noise on prices. In addition to isolating the impact of noise on the volatility, the discrete model enables us to extract the noise impact on the drift coefficient. We provide evidence for the primary microstructure noise we believe our empirical examples capture.

Problem

• Incorporating market microstructure noise into asset pricing models
• Developing continuous and discrete frameworks for option valuation
• Extracting noise impact coefficients on volatility and drift

Innovation

• Continuous-time model incorporating microstructure noise effects
• Discrete binomial tree extending Grossman-Stiglitz framework
• Unique martingale measure mapping real-world to risk-neutral dynamics