An empirical behavioral model of price formation
An empirical behavioral model of price formation
This paper develops an empirical behavioral model of price formation using high-frequency data from the London Stock Exchange. The authors analyze order placement and cancellation patterns, uncovering surprising regularities: the probability of placing a limit order at a given price relative to the best quote follows a symmetric Student distribution with less than two degrees of freedom, independent of the bid-ask spread and identical for buys and sells. This contradicts strategic reasoning that would predict asymmetry between orders inside the spread and inside the book. The fraction of orders that result in immediate transactions is accurately captured by the tail of this distribution. For cancellations, lifetimes follow a power-law distribution rather than an exponential, with rates depending on the order's distance to the opposite best price and the imbalance of buy/sell orders in the book. The authors combine these empirical findings with a long-memory model for order signs (based on strategic order splitting) into a stochastic representative agent simulation. Without fitting any parameters to price data, the model successfully reproduces the magnitude and functional form of return distributions and bid-ask spreads, including heavy tails. The work provides a quantitative behavioral alternative to rational equilibrium models, demonstrating that simple statistical regularities in order flow can explain key market properties.
Highlights
- 1Order placement probability is well approximated by a symmetric Student distribution with less than two degrees of freedom, independent of the bid-ask spread and identical for buy and sell orders.
- 2The fraction of orders resulting in transactions is accurately predicted by the tail of the Student distribution, matching empirical data across varying spreads.
- 3Order cancellation lifetimes follow a power-law distribution, with cancellation rates depending on order position relative to the best price and order book imbalance.
- 4A stochastic representative agent model combining empirical order placement, long-memory order signs, and cancellation reproduces the magnitude and functional form of return distributions and bid-ask spreads without parameter adjustment from price data.
Methods
- MEmpirical analysis of limit order book data from the London Stock Exchange (stocks AZN, LLOY, BLT) to estimate conditional probability distributions for order placement and cancellation.
- MKolmogorov-Smirnov tests to validate the Student distribution hypothesis for order placement across different spread bins.
- MLong-memory modeling of order signs using a fractional Gaussian process or a strategic order-splitting model with power-law distributed hidden order sizes.
- MSimulation of price formation using a stochastic agent-based model that incorporates empirical order placement, cancellation, and sign processes.
Results
- ROrder placement probability density p(x) is symmetric and follows a Student distribution with 1.3 degrees of freedom, independent of spread and order side.
- RThe transaction probability P_θ(s) derived from the Student distribution matches empirical data, approaching 0.5 as spread → 0 and 0 as spread → ∞.
- ROrder cancellation lifetimes exhibit power-law tails with exponents γ ≈ 1.1 (AZN), 1.55 (BLT), 1.19 (LLOY), deviating from exponential Poisson assumption.
- RThe simulation model predicts return distributions and bid-ask spreads that closely match real data, with power-law tails (though slightly heavier than observed).
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