The Cont-Stoikov-Talreja Book Model

A limit order book is really just several queues stacked on top of each other — one queue of resting size at each price level — where orders arrive, get filled, or get cancelled. The Cont-Stoikov-Talreja (CST) model treats the book exactly this way: it models the size at the best bid and best ask as independent birth-death processes, where "births" are new limit order arrivals adding to the queue and "deaths" are cancellations or executions removing from it, each happening at its own constant Poisson rate.

Given arrival rates for market orders, limit orders, and cancellations at the best levels, the model derives a closed-form expression for the probability that the next price move is an uptick versus a downtick, and for the expected time until the best bid or ask queue is exhausted. The intuition matches a simple queueing fact: a thin best-ask queue with a thick best-bid queue is more likely to be consumed first, since fewer arriving market sell orders are needed to empty it, making an uptick (ask exhausted, price moves up to the next level) more likely than a downtick.

The model's main value in practice is as a benchmark rather than a literal production forecaster — real order flow shows clustering and self-excitation that a plain birth-death process doesn't capture, so CST-style formulas are typically used to build intuition for how queue imbalance should relate to short-term price direction, with the exact rate estimates fitted or replaced by empirical or Hawkes-process models for live trading.