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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