The simplicity of optimal trading in order book markets

A trader's execution strategy has a large effect on his profits. Identifying an optimal strategy, however, is often frustrated by the complexity of market microstructure's. We analyse an order book based continuous double auction market under two different models of trader's behaviour. In the first case actions only depend on a linear combination of the best bid and ask. In the second model traders adopt the Markov perfect equilibrium strategies of the trading game. Both models are analytically intractable and so optimal strategies are identified by the use of numerical techniques. Using the Markov model we show that, beyond the best quotes, additional information has little effect on either the behaviour of traders or the dynamics of the market. The remarkable similarity of the results obtained by the linear model indicates that the optimal strategy may be reasonably approximated by a linear function. We conclude that whilst the order book market and strategy space of traders are potentially very large and complex, optimal strategies may be relatively simple and based on a minimal information set.