Sasha Stoikov

A Stochastic Model for Order Book Dynamics

We propose a continuous-time stochastic model for the dynamics of a limit order book. The model strikes a balance between three desirable features: it can be estimated easily from data, it captures key empirical properties of order book dynamics, and its analytical tractability allows for fast computation of various quantities of interest without resorting to simulation. We describe a simple parameter estimation procedure based on high-frequency observations of the order book and illustrate the results on data from the Tokyo Stock Exchange. Using simple matrix computations and Laplace transform methods, we are able to efficiently compute probabilities of various events, conditional on the state of the order book: an increase in the midprice, execution of an order at the bid before the ask quote moves, and execution of both a buy and a sell order at the best quotes before the price moves. Using high-frequency data, we show that our model can effectively capture the short-term dynamics of a limit order book. We also evaluate the performance of a simple trading strategy based on our results.

High-frequency trading in a limit order book

The role of a dealer in securities markets is to provide liquidity on the exchange by quoting bid and ask prices at which he is willing to buy and sell a specific quantity of assets. Traditionally,...

Forecasting Prices from Level-I Quotes in the Presence of Hidden Liquidity

Bid and ask sizes at the top of the order book provide information on short-term price moves. Drawing from classical descriptions of the order book in terms of queues and order-arrival rates (Smith et al., 2003), we consider a diffusion model for the evolution of the best bid/ask queues. We compute the probability that the next price move is upward, conditional on the best bid/ask sizes, the hidden liquidity in the market and the correlation between changes in the bid/ask sizes. The model can be useful, among other things, to rank trading venues in terms of the “information content” of their quotes and to estimate hidden liquidity in a market based on high-frequency data. We illustrate the approach with an empirical study of a few stocks using quotes from various exchanges

High Frequency Asymptotics for the Limit Order Book

We study the one-sided limit order book corresponding to limit sell orders and model it as a measure-valued process. Limit orders arrive to the book according to a Poisson process and are placed on the book according to a distribution which varies depending on the current best price. Market orders to buy periodically arrive to the book according to a second, independent Poisson process and remove from the book the order corresponding to the current best price. We consider the above described limit order book in a high frequency regime in which the rate of incoming limit and market orders is large and traders place their limit sell orders close to the current best price. Our first set of results provide weak limits for the unscaled price process and the properly scaled measure-valued limit order book process in the high frequency regime. In particular, we characterize the limiting measure-valued limit order book process as the solution to a measure-valued stochastic differential equation. We then provide an analysis of both the transient and long-run behavior of the limiting limit order book process.

Online algorithms in high-frequency trading

The challenges faced by competing HFT algorithms.

Reducing transaction costs with low-latency trading algorithms

We formulate a trade execution problem at the market microstructure level and solve it using dynamic programming. The objective is to sell a single lot of an asset in a short time horizon T, using the imbalance of the top of book bid and ask sizes as a price predictor. The optimization problem takes into account the latency L of the trading algorithm, which affects the prices at which the asset is traded. The solution divides the state space into a ‘trade’ and a ‘no-trade’ region. We calculate the cost of latency per lot traded and demonstrate that the advantage of observing the limit order book can dissipate quickly as execution latency increases. In the empirical section, we show that our optimal policy significantly outperforms a TWAP algorithm in liquidating on-the-run US treasury bonds, saving on average approximately 1/3 of the spread per share if trades are executed with low latency (1 ms).