Reducing Transaction Costs with Low-Latency Trading Algorithms

Sasha Stoikov and Rolf Waeber

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 as-
set 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 aff ects 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 signi ficantly outperforms
a TWAP algorithm in liquidating on-the-run U.S. treasury bonds, saving on average
approximately 1/3 of the spread per share if trades are executed with low latency
(1 millisecond). 

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The Price Impact of Order Book Events

Rama Cont, Arseniy Kukanov and Sasha Stoikov

We study the price impact of order book events - limit orders, market orders and cancelations - using the NYSE TAQ data for 50 U.S. stocks. We show that, over short time intervals, price changes are mainly driven by the order flow imbalance, defined as the imbalance between supply and demand at the best bid and ask prices. Our study reveals a linear relation between order flow imbalance and price changes, with a slope inversely proportional to the market depth. These results are shown to be robust to intraday seasonality effects, and stable across time scales and across stocks. This linear price impact model, together with a scaling argument, implies the empirically observed "square-root" relation between the magnitude of price moves and trading volume. However, the latter relation is found to be noisy and less robust than the one based on order flow imbalance. We discuss a potential application of order flow imbalance as a measure of adverse selection in limit order executions, and demonstrate how it can be used to analyze intraday volatility dynamics.

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High-Frequency Trading in a Limit Order Book

Marco Avellaneda and Sasha Stoikov

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, this role has been filled by marketmaker or specialist firms. In recent years, with the growth of electronic exchanges such as Nasdaq’s Inet, anyone willing to submit limit orders in the system can effectively play the role of a dealer. Indeed, the availability of high frequency data on the limit order book ensures a fair playing field where various agents can post limit orders at the prices they choose. In this paper, we study the optimal submission strategies of bid and ask orders in such a limit order book.

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A Stochastic Model for Order Book Dynamics

Rama Cont, Rishi Talreja and Sasha Stoikov

We propose a stochastic model for the continuous-time 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 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 mid-price, 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 that is based on our results.

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Online Algorithms in High-frequency Trading

Jacob Loveless, Sasha Stoikov and Rolf Waeber

HFT (high-frequency trading) has emerged as a powerful force in modern financial markets. Only 20 years ago, most of the trading volume occurred in exchanges such as the New York Stock Exchange, where humans dressed in brightly colored outfits would gesticulate and scream their trading intentions. Nowadays, trading occurs mostly in electronic servers in data centers, where computers communicate their trading intentions through network messages. This transition from physical exchanges to electronic platforms has been particularly profitable for HFT firms, which invested heavily in the infrastructure of this new environment.

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