Title:

Algorithmic trading : model of execution probability and order placement strategy

Most equity and derivative exchanges around the world are nowadays organised as orderdriven markets where market participants trade against each other without the help of market makers or other intermediaries as in quotedriven markets. In these markets, traders have a choice either to execute their trade immediately at the best available price by submitting market orders or to trade patiently by submitting limit orders to execute a trade at a more favourable price. Consequently, determining an appropriate order type and price for a particular trade is a fundamental problem faced everyday by all traders in such markets. On one hand, traders would prefer to place their orders far away from the current best price to increase their payoffs. On the other hand, the farther away from the current best price the lower the chance that their orders will be executed. As a result, traders need to find a right tradeoff between these two opposite choices to execute their trades effectively. Undoubtedly, one of the most important factors in valuing such tradeoff is a model of execution probability as the expected profit of traders who decide to trade via limit orders is an increasing function of the execution probability. Although a model of execution probability is a crucial component for making this decision, the research into how to model this probability is still limited and requires further investigation. The objective of this research is, hence, to extend this literature by investigating various ways in which the execution probability can be modelled with the aim to find a suitable model for modelling this probability as well as a way to utilise these models to make order placement decisions in algorithmic trading systems. To achieve this, this thesis is separated into four main experiments: 1. The first experiment analyses the behaviour of previously proposed execution probability models in a controlled environment by using data generated from simulation models of orderdriven markets with the aim to identify the advantage, disadvantage and limitation of each method. 2. The second experiment analyses the relationship between execution probabilities and price fluctuations as well as a method for predicting execution probabilities based on previous price fluctuations and other related variables. 3. The third experiment investigates a way to estimate the execution probability in the simulation model utilised in the first experiment without resorting to computer simulation by deriving a model for describing the dynamic of asset price in this simulation model and utilising the derived model to estimate the execution probability. 4. The final experiment assesses the performance of utilising the developed execution probability models when applying them to make order placement decisions for liquidity traders who must fill his order before some specific deadline. The experiments with previous models indicate that survival analysis is the most appropriate method for modelling the execution probability because of its ability to handle censored observations caused by unexecuted and cancelled orders. However, standard survival analysis models (i.e. the proportional hazards model and accelerated failure time model) are not flexible enough to model the effect of explanatory variables such as limit order price and bidask spread. Moreover, the amount of the data required to fit these models at several price levels simultaneously grows linearly with the number of price levels. This might cause a problem when we want to model the execution probability at all possible price levels. To amend this problem, the second experiment purposes to model the execution probability during a specified time horizon from the maximum price fluctuations during the specified period. This model not only reduces the amount of the data required to fit the model in such situation, but it also provides a natural way to apply traditional time series analysis techniques to model the execution probability. Additionally, it also enables us to empirically illustrate that future execution probabilities are strongly correlated to past execution probabilities. In the third experiment, we propose a framework to model the dynamic of asset price from the stochastic properties of order arrival and cancellation processes. This establishes the relationship between microscopic dynamic of the limit order book and a longterm dynamic of the asset price process. Unlike traditional methods that model asset price dynamic using onedimensional stochastic process, the proposed framework models this dynamic using a two dimensional stochastic process where the additional dimension represents information about the last price change. Finally, the results from the last experiment indicate that the proposed framework for making order placement decision based on the developed execution probability model outperform naive order placement strategy and the best static strategy in most situations.
