Abstract
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 microstructures. We analyse an order book based on 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 while 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.
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Notes
- 1.
We never cancel the order in the time step in which it is submitted.
- 2.
We always use the standard price-time priority to break ties.
- 3.
We also consider a special case where \(l=0\). In this case prices are selected at random uniformly from the distribution \((0,v_{i})\) for buyers and \((c_{j},\overline{A})\) for sellers. This constitutes a Zero Intelligence (ZI) strategy as defined by Gode and Sunder (1993).
- 4.
Every 100,000 time steps we set \(m_{t}^{b,S}=1,\forall b,S\). Moreover, with probability \(p_{R}\) rather than submitting the utility maximising order a trader instead submits a randomly chosen order in the current configuration. The effect of this is to help prevent local equilibrium. In particular, due to poor early performance, certain actions may no longer be chosen, however, as strategies are refined over time these orders may be once again acceptable. The random selection of these orders allows them to be reintroduced to the strategy.
- 5.
States are obtained from 20 independent simulations of 7 days of trading. We approximate a continuous flow of traders using a large population of 760 agents, 380 buyers and 380 sellers: hence, statistics are based on \(106,400=20\times 7\times 760\) states.
- 6.
The quantities at the best quotes for the linear model are not given as with continuous pricing there is never more tha one order at this price.
- 7.
The effect of the width of the price grid—the number of ticks in the market—was also considered. Doubling the number of ticks in the price grid led to an increase in the spread of \(50\,\%\) while the quantities at the best quotes were found to be \(50\,\%\) greater under the smaller set of prices. Importantly, however, a larger price grid was found to have no effect on the behaviour of the model across information levels, that is, for all information levels the spread and quantities available were the same.
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Ladley, D., Pellizzari, P. (2014). The Simplicity of Optimal Trading in Order Book Markets. In: Dieci, R., He, XZ., Hommes, C. (eds) Nonlinear Economic Dynamics and Financial Modelling. Springer, Cham. https://doi.org/10.1007/978-3-319-07470-2_11
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DOI: https://doi.org/10.1007/978-3-319-07470-2_11
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