A maximum-entropy 'Boltzmann price' family interpolates between mid-price and weighted mid-price, and its imbalance-driven dynamics generate fat-tailed price changes that broadly resemble historical equity data.
Trade arrival dynamics and quote imbalance in a limit order book
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abstract
We examine the dynamics of the bid and ask queues of a limit order book and their relationship with the intensity of trade arrivals. In particular, we study the probability of price movements and trade arrivals as a function of the quote imbalance at the top of the limit order book. We propose a stochastic model in an attempt to capture the joint dynamics of the top of the book queues and the trading process, and describe a semi-analytic approach to calculate the relative probability of market events. We calibrate the model using historical market data and discuss the quality of fit and practical applications of the results.
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Boltzmann Price: Toward Understanding the Fair Price in High-Frequency Markets
A maximum-entropy 'Boltzmann price' family interpolates between mid-price and weighted mid-price, and its imbalance-driven dynamics generate fat-tailed price changes that broadly resemble historical equity data.