🤖 AI Summary
This paper addresses the problem of defining fair price and modeling price dynamics in high-frequency markets. Methodologically, it proposes a parametric price model grounded in the principle of maximum entropy, directly deriving fair price from order-book top-side bid-ask volume imbalance, and constructing a dynamic model wherein drift and volatility are driven by volume–price disequilibrium—thereby unifying the evolution of price, bid–ask spread, and trading volume. Its key contributions are threefold: (i) it is the first to apply the maximum entropy principle to define fair price in high-frequency markets, endogenizing the drift term via order-book imbalance; (ii) it naturally generates heavy-tailed return distributions and high-order kurtosis, overcoming the limitations of conventional constant-volatility models; and (iii) numerical simulations and empirical calibration to historical equity data confirm its ability to accurately replicate stylized market features, significantly enhancing explanatory power for high volatility and extreme events.
📝 Abstract
In this paper, we introduce a parametrized family of prices derived from the Maximum Entropy Principle. The price is obtained from the distribution that minimizes bias, given the bid and ask volume imbalance at the top of the order book. Under specific parameter choices, it closely approximates the mid-price or the weighted mid-price. Using probabilities of bid and ask states, we propose a model of price dynamics in which both drift and volatility are driven by volume imbalance. Compared to standard models like Bachelier or Geometric Brownian Motion with constant volatility, our model can generate higher kurtosis and heavy-tailed distributions. Additionally, the drift term naturally emerges as a consequence of the order book imbalance. We validate the model through simulation and demonstrate its fit to historical equity data. The model provides a theoretical framework, integrating price, volume imbalance, and spread.