Abstract — The problem of optimal order execution has been a main concern for financial trading and brokerage firms for decades. The idea of executing a client’s order to buy or sell a pre-specified number of shares at a price better than all other competitors seems intriguing. This paper introduces a system that utilises fuzzy logic in order to capture the current market condition generated by the accumulation of momentum. The proposed fuzzy logic momentum analysis system outperforms the traditional systems used in industry, which are often based on executing orders dependent on the weighted average of the current volume. The system proves that, on average, it increases profitability on orders on both the buy and sell sides. Index Terms — Fuzzy Logic, High Frequency Trading, Momentum Analysis, Order Execution. I. INTRODUCTION High frequency trading holds a rapidly growing interest both for researchers and financial investment entities. Finding better order execution rates is an intriguing problem. For brokers trading large orders, the effect of order size and the market’s trend and volatility are crucial for order scheduling [10]. The cumulated order quantity of these institutional traders usually represents a big proportion of the daily trading volume, requiring sophisticated order splitting mechanisms to reduce market impact. This paper proposes a new framework for high frequency order execution using a novel way of momentum analysis which makes use of fuzzy logic reasoning mechanisms. The suggested order placement algorithm also considers the market’s intraday volatility to minimize trading costs. The modelling of financial systems continues to hold great interest not only for researchers but also for investors and policymakers. Many of the characteristics of these systems, however, cannot be adequately captured by traditional financial modelling approaches. Financial systems are complex, nonlinear, dynamically changing systems in which it is often difficult to identify interdependent variables and their values. However, this involves the implementation of a system that considers the whole price formation process from a different point of view. Financial brokers profit from executing clients’ orders of buying and selling of certain Manuscript received November 3, 2010. A. Kablan is with the Centre for Computational Finance and Economic Agents, University of Essex, Wivenhoe Park, Essex, CO4 3SQ, United Kingdom (e-mail: akabla@essex.ac.uk). W. L. Ng is a lecturer in High-Frequency Finance at the Centre for Computational Finance and Economic Agents, University of Essex, Wivenhoe Park, Essex, CO4 3SQ, United Kingdom (e-mail: wlng@essex.ac.uk). amounts of shares at the best possible price. Many mathematical and algorithmic systems have been developed for this task [7], yet most of them can not overcome a standard volume based system. Time series models were first combined with fuzzy theory [20]-[21], resulting in fuzzy time-series, which is the fundamental framework of all of the investment systems. These authors detail five steps for such a system: 1. Definition and partition the universe of discourse. 2. Definintion the fuzzy sets. 3. Fuzzifying the observations. 4. Establishing the fuzzy relationships. 5. Forecasting and defuzzifying the results. Researchers creating stock trading systems have implemented many variations of this model, of which the key adaptation primarily concerns the selection of appropriate observations, the definition of the fuzzy relationships, and the particular inference system used for forecasting. Most systems use well-documented technical indicators from financial theory for their observations. For example, [9] used three technical indicators in their stock trading system: the rate of change, the stochastic momentum indicator and a support-resistance indicator that is based on the thirty-day price average. A convergence module then maps these indices as well as the closing price on to a set of inputs for the fuzzy system, thus providing a total of seven inputs. In some cases, such as the rate of change, an indicator maps to a single input. However, it is also possible to map one indicator to multiple inputs. Four levels of quantification for each input value are used: small, medium, big and large. Mamdani’s form of fuzzy rules [18] can be used to combine these inputs and produce a single output variable with a value between 0 and 100. Low values indicate a strong sell, and high values a strong buy. The system is evaluated using three years of historical stock price data from four companies with variable performance during one period and employing two different strategies (risk-based and performance-based). In each strategy, the system begins with an initial investment of $10,000 and assumes a constant transaction cost of $10. Similarly, tax implications are not taken into consideration. The resulting system output is shown to compare favourably with stock price movement, outperforming the S&P 500 in the same period. The application presented in this study differs from the above, as it introduces a fuzzy logic-based system for momentum analysis [17]. The system uses fuzzy reasoning to analyse the current market conditions according to which a certain equity’s price is currently moving. This is then used as a trading application. First, the membership functions were decided by the expert-based method but then later optimized using ANFIS to further improve the trading performance. Enhancing High-Frequency Order Placement Strategies with Fuzzy Logic and Fuzzy Inference Abdalla Kablan Member, IAENG, and Wing Lon Ng IAENG International Journal of Computer Science, 37:4, IJCS_37_4_06 (Advance online publication: 23 November 2010) ______________________________________________________________________________________