High frequency trading is a new topic which proposed in 1999 just after the US Securities and Exchange Commission (SEC) permitting electronic exchanges. Although high frequency trading only captures less than 10% of equity trades in early 2000, it grows rapidly during the subsequent years. According to data from NYSE, high frequency trading grew by 164% between 2005 and 2009. And by 2010 high frequency trading captures over 70% of equity trades in US market and growing rapidly in Europe and Asia market (Wikipedia1). High frequency traders usually compete with other high frequency traders instead of long-term investors whose investment last a period of weeks, months or even years. Firms make high frequency trade in just microseconds or even one-millionth of a second. Although they only intend to obtain very small or even negligible profits per unit on every trade, repeated trade during a short time may lead to high frequency trading be highly risky. Nowadays, high frequency trading brokers usually adopt standard volume based trading system to make order execution. This commonly used system will execute a buy or sell order at a constant percentage if the total volume in the market is enough without considering other factors. This traditional method is not coincide with our common sense which increases the buy order when price is low and decreases the buy order when price is high.
The reason why high frequency trading is concerned by increasing number of investors and researchers is because of its benefits which include improving market liquidity, lowering the transaction costs and spreading some information of quotes to financial market. Apart from benefits, it also has some challenges such as, enormous amount of intra-day data, financial signals are not easy to be captured and the need of executing orders rapidly, can lead to more risks. Since its challenges, traditional approaches such as standard volume based trading system may not work well and a more accurate system needs to be investigated. Recent research suggests applying the combination of fuzzy logic and technical analysis into developing financial investment systems, because fuzzy logic can improve the accuracy of evaluating stock price movement (Dourra, H and Siy, P). The fuzzy logic momentum analysis system introduced in this report firstly calculates momentum of stock price movement and then determines various participation rates under different market conditions which can be classified into seven levels which include extremely strong, strong, slightly strong, stable, slightly weak, weak and extremely weak according to the calculating result of momentum. We also use MATLAB to compute momentum and analysis fuzzy inference system. Furthermore, adaptive neuro network will be adopted to make the analysis more accurate through optimize the membership function of fuzzy inference system. This new method can overcome the weakness of traditional standard volume based trading system which execute buy or sell order at a certain amount.
The main problem concerned by brokerage firms is when to execute a buy or sell order and how many shares to buy or sell in high frequency trading. To simplify the problem, transaction costs and tax costs are not taken into consideration in this report. The purpose of this report is to demonstrate that fuzzy logic momentum analysis system can perform better than standard volume based trading system adopted popularly by many financial investment organizations and brokerage firms around the world. The method of comparison these two systems is to calculate the average stock price of China Ping An Insurance Company and China Pacific Insurance Company in each simulation of buying or selling 1 million shares of each and the lower the average price, the better the system. We will also demonstrate that adaptive neuro fuzzy inference system is more effective than fuzzy inference system.
The next section introduces some mathematical theories and tools, such as fuzzy logic, fuzzy set, fuzzy inference systems, adaptive neuro fuzzy inference system and some knowledge of MATLAB. Section III describes standard volume based trading system and fuzzy logic momentum analysis system in detail. Data observed from two stocks chosen from China Ping An Insurance Company and China Pacific Insurance Company is described and analyzed in section IV. Section V compares standard volume based trading system and fuzzy logic momentum analysis system. A conclusion of this report is presented in section VI.
II. Mathematical Theories and Tools
Fuzzy Logic and Fuzzy Set
Fuzzy logic which was first developed by Lotfi A. Zadeh in 1965 is an extension of two-valued logic, which extending the binary pair {0, 1} to the whole continuous interval [0, 1]. The traditional two-valued logic has only two truth values 1 and 0 which represent True and False, respectively. However, sometimes there exists a third possibility which between True and False, such as maybe true. Fuzzy logic can solve the problem of inadequacy of traditional logic when describing human reasoning (Hellmann, M.). The essential features of fuzzy logic are as follows (MathWorks):
Fuzzy logic is based on ordinary language used by people on daily communication.
Fuzzy logic can be built according to experiences of experts.
Fuzzy logic can process imprecise data with a matter of degree since it is approximate reasoning rather than exact.
Fuzzy logic is a powerful tool for dealing with nonlinear functions of arbitrary complexity.
Fuzzy set is a further development of crisp set which is well-known by people. To describe the fuzzy set clearly, Zadeh proposed a definition of grade of membership which cancel the strict boundary between membership and non-membership so that it can transfer from membership to non-membership gradually rather than abruptly. A fuzzy setcan be expressed as where is the universe of discourse whose elements are represented by and is called the membership function of in fuzzy set. Membership function is an arbitrary curve on which each point represent the magnitude of participation of each input, and it can be continuous or discrete, such as, bell-shaped, triangular or trapezoidal (Jantzen,J.). The only limit of membership function is that its value must vary between 0 and 1. 0 means that the element is not included in the fuzzy set, and 1 indicated that the element is fully included.
There are some basic operations on fuzzy sets (Jantzen, J). Let A and B be fuzzy sets on a mutual universe, it can be inferred that:
1. The intersection of A and B is
2. The union of A and B is
3. The complement of A is
4. A fuzzy set X is a fuzzy subset of set Y, written, which means that the membership function of X is less than or equal to that of Y. Furthermore, it can be written that.
5. Modifiers. Linguistic modifier, such as a little, more or less, very or extremely is an operation that can change a term's degree of meaning. Take a term a as a example,very , extremely ,slightly . All the modifiers can be described by where p is between 0 and infinity. When p=, means exactly.
Fuzzy Inference Systems
Fuzzy inference systems also called fuzzy-rule-based systems or fuzzy associated memories (FAM) are a process of obtaining a crisp output from a given crisp input. This system involves a number of fuzzy if-then rules, membership functions of fuzzy sets, logical operations, fuzzification which transforms the crisp input into fuzzy input qualified in linguistic values and defuzzification which transforms the fuzzy output into crisp output, the adverse process of fuzzification (Jang, R.).
If-then rules play a very important role in fuzzy inference system. For example, if x is A then y is B, where both A and B are linguistic values defined by fuzzy sets on X and Irrespectively. The part's is A" is called antecedent, and the rest part "y is B" is called consequent. If the antecedent is true to some degree of membership, then the consequent part is also true to the same degree. Moreover, both antecedent and consequent can contain multiple parts connected with words called connectives such as and, or. The word "and" is used to join two sentences to form conjunction, similarly, "or" can also join two sentences which are called disjunction.
There are many territories such as data classification, decision analysis and so on which make use of fuzzy inference systems (MathWorks). In general, fuzzy inference system is comprised of five steps:
Fuzzification of the input. This step is to transform the crisp input into fuzzy input qualified in linguistic values by membership functions required by rules.
Using of fuzzy logical operations. Fuzzy operators, that is, AND or OR are employed when the rule contains more than one precondition.
Determine the weight of each rule and application of implication method. Since not all the rules have the same influence on system behavior that is some rules may be more important than others, to deal with this problem, a weight of each rule need to be defined. The maximum weight is 1, and the minimum is 0.
Combination of all the output of each rule. A single fuzzy set is obtained via the aggregation of all the output of each rule with the weight of each output value.
Defuzzification the output. Defuzzification transforms the fuzzy output into crisp output which is a single number. There are five method of defuzzification: centroid, bisector, middle of maximum, largest of maximum, and smallest of maximum.
These five steps of fuzzy inference system can be presented using process flow chart (Figure1).
Logical operations
Crisp Input Fuzzification Fuzzy Input
Defuzzification
Determine the weight of each rule
Fuzzy output
Crisp output
Figure1: the stages of fuzzy inference system
There are many kinds of fuzzy inference systems that have been proposed in previous literatures. Almost all of the fuzzy inference systems can be classified into three types according to different types of fuzzy reasoning and different fuzzy if-then rules used. The first type of fuzzy inference systems is the Sugeno model in which the overall output is the weighted aggregation of each rule's output value. It can be used to model any inference system because its output membership functions are either linear or constant. Its rules have forms of "If x is A and y is B, then z=f(x, y) where A and B are fuzzy sets and f(x, y) consists of liner combination of x and y and also a constant term".
If x is A1 and y is B1, then f1=p1x+q1y+r1
If x is A2 and y is B2, then f2=p2x+q2y+r2
The weight of the first rule is w1 and the weight of the second rule is w2, so the final output which is the weighted average of each rule's crisp output formulated.
The second type is Tsukamoto fuzzy model which is similar with Sugeno model except the monotonic membership functions instead of linear or constant. For example, the two rules of Tsukamoto fuzzy model is "If x is A1 and y is B1, then f1=p1x+q1y+r1；If x is A2 and y is B2,then f2=p2x+q2y+r2" and the weights of the two rules are w1 and w2 respectively。Then the final output is.
The third type is Mamdani fuzzy model which can model a complicated no-linear system via the use user-defined fuzzy rules which can be easily defined by humans (Bryan Davis).Mamdani fuzzy model uses min and max for T-norm and T-conorm operators, respectively. When analyzing complicated financial problems, Mamdani fuzzy model is a better choice to use.
Adaptive Neuro Fuzzy Inference System
There exist some drawbacks in fuzzy inference system, for example, human knowledge and experience cannot be added to fuzzy if-then rules and membership functions of fuzzy set, and the output error can be reduced by a method of fine tuning membership functions (Jang, R.). Furthermore, fuzzy inference system only considers the qualitative aspect without accurate quantitative analysis. To optimize fuzzy inference system, adaptive networks need to be employed. An adaptive network is a multilayer network structure with directional links and two kinds of node, square node (adaptive node) with parameters and circle node (fixed node) without parameters. Adaptive means that parameters connected with nodes will affect the output of these nodes and these networks linking nodes make the relationships between input and output clearly. The merger the fuzzy inference system with the framework of adaptive networks is called Adaptive Neuro Fuzzy Inference System (ANFIS) which is functionally equivalent to fuzzy inference systems (Jang, R.). Figure2 shows the process flow chart of the stages of Adaptive Neuro Fuzzy Inference System. Compared with Figure1 above, it can be found that the process of these two systems is almost the same except knowledge and experiences are needed in ANFIS. ANFIS provides an approach which allows us to learn information about data set in order to track it via computing the parameters of membership function. Figure3 illustrates a first order Sugeno fuzzy inference system with two inputsand, two membership functions of fuzzy sets (Ai, Bi, i=1, 2) and, two rules and one output.
Rule 1: If x is A1 and y is B1, then f1=p1x+q1y+r1
Rule 2: If x is A2 and y is B2, then f2=p2x+q2y+r2
There are five layers of ANFIS Architecture introduced in the following (Jang, R.):
Layer1: Adaptive nodes in this layer refer to membership function for inputsand:
If we choose bell-shaped membership functions as and, their equations are as follows: where are premise parameters which need to be determined. The membership function will change according to the changes of these premise parameters. If we choose other type membership functions, they will also change on the basis of their parameters.
Layer2: The output of circle nodes indicates the firing strengths of each rule calculated by
Layer3: Fixed nodes in this layer represent normalized firing strengths which is the ratio of the firing strengths to the all rules' firing strengths.
Layer4: square nodes in this layer refer to the consequence of the two rules, and node function is
, where are called consequence parameters.
Layer5: a single fixed node in this layer computer the overall output using the summation equation:
Knowledge and experience
Defuzzification
Inference
Fuzzification
Crisp input Crisp output
Figure2: stages of Adaptive Neuro Fuzzy Inference System
A1
Layer1 Layer2 Layer3 Layer4 x y
A2
X layer5
B2
B1
Y
x y
Figure3: ANFIS Architecture for two inputsand
Foundation of MATLAB
MATLAB is a key tool of investigating the fuzzy logic momentum analysis system of high frequency trading in this report since it can process very enormous amount of intra-day data and solve the problems of fuzzy logic. MATLAB which is the abbreviation of matrix laboratory is a kind of commercial mathematic software developed by MathWorks. It can be applied into many other fields which include engineering, science and economics due to its powerful matrix manipulations functions, analyzing and plotting data functions as well as other numerical computing. MATLAB becomes more convenient to operate when adding many kinds of toolboxes, such as fuzzy logic toolbox, signal processing toolbox (Wikipedia2). The major toolbox we will use is fuzzy logic toolbox which is one of numerous toolboxes built on the MATLAB numerical computing environment to design and edit fuzzy inference systems based on fuzzy logic. This toolbox provides three types of tools: the first is command line functions which have the same role as MATLAB code; the second is graphical interactive tools which use for designing, analyzing and implementing fuzzy inference system; the third is a set of Simulink blocks which are designed for high speed fuzzy logic inference in Simulink environment. By using this toolbox, we will not write and input complex MATLAB code and can get result easily. There are two types of fuzzy inference systems: Sugeno model and Mamdani model and eleven built-in membership function types based on some basic functions are contained in this toolbox. For example, triangular membership function is built on piecewise linear functions and generalized bell membership function is built on the Gaussian distribution function. Fuzzy logic toolbox can also classify the fuzzy inference process into five parts: fuzzifying inputs, applying fuzzy operator, applying implication method, aggregating all outputs and defuzzifying (MathWork). Furthermore, this toolbox also includes adaptive neuro fuzzy inference system which can be used to optimize membership function.
III. Methodology
Traditional systems applied in high frequency trading: Standard Volume Based Trading System (SVBTS)
Standard volume based trading system which is used for high frequency order execution is widely adopted in the financial market all over the world. It is based on a constant participation rate, that is, the system will execute a buy or sell order at a constant percentage if the total volume in the market is enough. Participation rate can be defined as a ratio between the amount of shares of a stock bought or sold at each trade and the total volume shares of the stock available in the market at that moment. Assume the total volume of shares of the stock currently in the market is where representing the times of trade, the constant participation rate is and the amount of shares need to be traded is. If is larger than, then the amount of shares sold or bought equals multiplies. And the total costs of this system equals to the summation of price multiplies the amount of shares of each trade (). However, if is less than, then order of buy or sell will not be executed. For example, a stock broker want to buy a total amount of 1 million of shares of a stock, the participation rate can be assumed to be 25%. Once stock volume is enough, the system will make a buy order of 25%* 1 million shares and the trade will be terminated when the accumulated sum is equal to 1 million. The sell order can operate the same as the buy order.
Standard volume based trading system using the constant participation rate does not take some external factors into consideration, such as market condition. Under this system orders are divided into several parts and executed randomly. Although standard volume based trading system does not capture many characteristics of financial signals, almost all financial brokers and traders of high frequency trading still use this system because no other approach which has been found can work better. Therefore, we will introduce a new system which may work better than the traditional one in the report.
A New System: Fuzzy Logic Momentum Analysis System (FULMAS)
An obvious disadvantages of standard volume based trading system is the fixed participation rate at any market conditions, fuzzy logic momentum analysis system can be employed to overcome this weakness. This system uses fuzzy logic and neural network knowledge to investigate on when to buy or sell and how many shares to trade in the trade of high frequency. Participation rate in fuzzy logic momentum analysis system can be determined by market condition no matter whether the total volume in the market is sufficient or not. This new system can be divided into four steps: momentum calculation, defining different market conditions, determining participation rate and applying the calculated result of momentum as crisp value into fuzzy system using the toolbox of MATLAB.
Firstly, using MATLAB program to calculate momentum on the basis of past price movement. Let be the current price of a stock, be the previous stock price and be a counter which will increase one unit ,decrease one unit or remain unchanged each time when price changes. If price goes up, which means is more than, then the counter will increase one unit. Similarly, if price goes down, that is, is less than, then the counter will reduce one unit (increase minus one unit). If price remains stable, the counter will add zero. Momentum can be expressed by the summation of on each time of price observation (), where is the total amount of ticks during the observed period of time. For example, if we want to estimate the general up or down trend of price changes after ticks, we can add all ticks according to its fluctuation using the calculation methods of momentum mentioned above. Since there are usually huge number of data needed to be processed in practice, MATLAB is very helpful mathematic software to process these enormous data very easily. The following program can be used to calculate momentum processed in MATLAB.
>> k=0;
>> for i=2:100
if p(i)>p(i-1)
k(i)=k(i-1)+1
elseif p(i)<p(i-1)
k(i)=k(i-1)-1
else
k(i)=k(i-1)+0
end
end
Program of calculating momentum
Secondly, we need to define financial market conditions. After computing the momentum of price observation during an observed period, market conditions need to be defined to describe all possible price fluctuations. Market conditions which can be indicated by momentum can be divided into seven grades using linguistic values on the basis of the extent of price movement. In this report, these seven kinds of market conditions can be defined as extremely strong, strong, slightly strong, stable, slightly weak, weak and extremely weak. When applying the momentum in the market conditions, adding more ones than minus ones or zero means that the condition of market is stronger, subtracting more ones means that market is weaker and more zeros implies that market is more stable.
Thirdly, participation rate needs to be determined. Different participation rates can be determined according to corresponding market conditions which can be classified via analyzing the momentum of stock price movement. On the basis of our common sense, the stronger the market, the higher price of a stock and so the lower the participation rate when making buy order. On the contrary, the stronger the market, the higher the participation rate when selling stocks. For example, as shown in following Table 1, the participation rate of a selling party is about 40% under extremely strong market but only 10% for a buying party. When the market is stable, the participation rate of a selling party will reduce to 25% and increase to 25% for a buying party. When market is extremely weak, the participation rate of a selling party will continue to reduce to 10% and increase to 40% for a buying party. Assume participation rate is under different market conditions, where, (different m represents different market conditions) and the total volume of shares need to be transacted is. Therefore, the amount of shares sold or bought using fuzzy logic momentum analysis system is multiplies T (*T) and the total costs can be calculated by the summation of price multiplies the amount of shares of each trade ().
The final step of fuzzy logic momentum analysis system is to input the calculated result of momentum as crisp value to the fuzzy system and to detect which position it will locate in the membership function. When determine which membership function will be used, we have several methods, such as expert-based method, automatic method and statistical methods. In this report, we use expert-based method also called psychological method which chooses membership function according to expert's suggestions. Therefore we choose triangular membership function since its mathematical simplicity. Triangular membership function can be presented as, it only requires there parameters and can be modified by altering these three parameters. Figure 6 shows the membership functions of triangular. To make FULMAS work more efficiency, we can apply the neural network into fuzzy logic inference, which is ANFIS mentioned above. We can utilize training data and desired outputs to improve membership functions. Figure 7 indicates the improved triangular and bell-shaped membership functions.
Market condition
Selling Party PR
Buying Party PR
Extremely Strong
40%
10%
Strong
35%
15%
Slightly Strong
30%
20%
Stable
25%
25%
Slightly Weak
20%
30%
Weak
15%
35%
Extremely Weak
10%
40%
Table 1 Participation rate of selling and buying parties in different market conditions under fuzzy logic momentum analysis system
Figure 6: Triangular membership functions without using ANFIS
Figure 7: Triangular membership functions optimized with ANFIS
IV. Data Description
In order to demonstrate that fuzzy logic momentum analysis system can perform better than standard volume based trading system, it is necessary to apply some stocks into these two systems. Stocks of China Ping An Insurance Company (sh:601318) and China Pacific Insurance Company (sh:601601) were chosen and data were recorded from 9:30 to 15:00 on March 30, 2011 at one minute interval and each stock can be offer 242 prices in total. The following figure 4 and figure 5 show the time series of share price for these two insurance companies, respectively. We need to select 100 ticks in sequence randomly from the 242 observations in order to simulate this actual situation, because stock brokers often make order execution at irregular spacing time in practice. Therefore, one significant feature of data in this report is irregularly spaced with random quotes at very short time which is different from traditional low-frequency regularly spaced data (Aldridge, I.).
Since we want to compare these two systems, we need to ensure they are in the same conditions. In other words, a new order execution will start again where the last execution of both systems has been finished. We also assume that there are enough shares to satisfy the need of high frequency trading. We will terminate order execution when buying or selling 1 million shares for each. The total amount simulation is 25 for each stock and each system.
Figure 4: Time series of share price for China Ping An Insurance Company from 9:30 to 15:00 on March 30, 2011.
Figure 5: Time series of share price for China Pacific Insurance Company from 9:30 to 15:00 on March 30, 2011.
V. Empirical Application
In this section, stocks of China Ping An Insurance Company and China Pacific Insurance Company will be taken as examples to demonstrate that Fuzzy Logic Momentum Analysis System will win Standard Volume Based Trading System and optimized Fuzzy Logic Momentum Analysis System can work better. As these two systems have been introduced in the previous section in detail, we will not repeat again. However, a criterion is needed to compare these systems.
Comparison between These Two Trading Systems
In order to assess whether FULMAS is more effective than SVBTS, a benchmark is needed to test the performance of these two systems. We can calculate the outperformance (OP) of FULMAS on the SVBTS in basis points according to the comparison of their order execution costs for buy and sell orders using the following formulas:
, where FULMAS price and SVBTS price can be defined as the total cost or revenue when buying or selling a specified volume of shares using FULMAS and SVBTS, respectively. FULMAS is better if the outperformance rate is positive both on buy and sell side.
Results
FULMAS VS SVBTS
After 25 simulations being carried on the 100 tick data set, we can get the FULMAS price as well as SVBTS price of each simulation, respectively. Then the outperformance rate can be calculated by using the outperformance formula. According the positive or negative result of outperformance rate, we can determine which system is better. Table 2 indicates that the average outperformance rate of buying 1 million shares of China Pacific Insurance Company is about 11.5 basis points, which means that using FULMAS can save 11.5 basis points of cost on average when buying shares of Pacific Insurance Company. Similarly, when buying shares of China Ping An Insurance Company, we can save approximately 3.7 basis points of cost when using FULMAS compared with SVBTS. For the selling side, we can find that FULMAS still has advantage in comparison with SVBTS. Besides the mean of outperformance rate, we also have other indicators, such as, the median. Form the following table 2 it can be found that the median is positive for both Pacific Insurance Company and Ping An Insurance Company regardless of buying and selling side. The positive median implies that FULMAS outperforms over SVBTS in more than half of simulations.
Optimized FULMAS VS SVBTS
Exactly as the comparison of FULMAS and SVBTS, optimized FULMAS and SVBTS were compared through 25 simulations which were carried on the same 100 tick data set and each simulation was ended up with execution 1 million shares. The comparison result is presented in table 3. This table implies that using the optimized FULMAS can save 11.67 basis points of cost on average when buying shares of Pacific Insurance Company. This data is 0.17 basis points higher than that of FULMAS, which means that optimized FULMAS is better than FULMAS. If buying shares of China Ping An Insurance Company, we can save approximately 4.15 basis points of cost when using optimized FULMAS and it also works better than FULMAS. Similarly, when making sell order, optimized FULMAS still has strength. Therefore, it can be concluded that optimized FULMAS is a better choice when making high frequency trading.
Mean
Median
Standard deviation
Skewness
Kurtosis
Buying Pacific
11.50295
11.89799
20.68173
0.48444
0.356215
Buying ping An
3.704487
4.320439
13.29386
-0.37366
-0.74396
Selling Pacific
6.685738
8.770419
17.582
-0.3676
-0.06009
Selling Ping An
9.519645
10.55176
9.098918
-0.58389
0.62269
Table 2 outperformance results of FULMAS on the SVBTS in basis points when buying and selling 1 million shares of China Ping An Insurance Company and China Pacific Insurance Company
Mean
Median
Standard deviation
Skewness
Kurtosis
Buying Pacific
11.67052
10.95091
20.55051
0.536961
0.397745
Buying ping An
4.145068
5.014581
13.094893
-0.3666766
-0.7250703
Selling Pacific
12.35905
13.00586
18.08108
-0.34931
-0.00794
Selling Ping An
10.28272
10.34631
9.230987
-0.51413
0.526428
Table 3 outperformance results of optimized FULMAS on the SVBTS in basis points when buying and selling 1 million shares of China Ping An Insurance Company and China Pacific Insurance Company
Figure 8: FULMAS outperformance to SVBTS in basis points when buying 1 million shares of China Pacific Insurance Company
Figure 9: optimized FULMAS outperformance to SVBTS in p basis points when buying 1 million shares of China Pacific Insurance Company
Figure 10: FULMAS outperformance to SVBTS in basis points when selling 1 million shares of China Pacific Insurance Company
Figure 11: optimized FULMAS outperformance to SVBTS in basis points when selling 1 million shares of China Pacific Insurance Company
Figure 12: FULMAS outperformance to SVBTS in basis points when buying 1 million shares of China Ping An Insurance Company
Figure 13: optimized FULMAS outperformance to SVBTS in basis points when buying 1 million shares of China Ping An Insurance Company
Figure 14: FULMAS outperformance to SVBTS in basis points when selling 1 million shares of China Ping An Insurance Company
Figure 15: optimized FULMAS outperformance to SVBTS in basis points when selling 1 million shares of China Ping An Insurance Company
VI. Conclusion
High frequency trading is concerned by more financial trading and brokerage firms as well as some researchers due to both its great benefits and difficult challenges. Though high frequency trading can improve market liquidity, decrease transaction costs and make information spread rapidly in financial market, it also leads to more risks deriving from the difficulty of capture financial signals and timing of execution orders. Nowadays, standard volume based trading system which executes orders at certain participant rate is widely used by almost all financial brokers of high frequency trading. However, this system cannot satisfy the complex and fast-moving financial market. In this report, we have presented a new mechanism called fuzzy logic momentum analysis system for high frequency trading. This new mechanism can execute orders at alterable participant rates according to market conditions. Furthermore, fuzzy logic momentum analysis system can be improved by applying Adaptive Neuro Fuzzy Inference System which allows us to modify membership function by tracking the information of data set. By applying stocks of China Ping An Insurance Company and China Pacific Insurance Company into these two mechanisms, it can be found that fuzzy logic momentum analysis system works better than standard volume based trading system and using ANFIS can optimize fuzzy logic momentum analysis system further. Therefore, we recommend the stock broker to use the fuzzy logic momentum analysis system instead of the traditional standard volume system.
There also exist some drawbacks of the fuzzy logic momentum analysis system introduced in this report. The only factor taken into consideration is price momentum. However, many other factors also exert influence. For example, we ignore impact costs. When large amount of shares are traded in a very short time, stock price will drive up or drive down suddenly and stock brokers cannot transact at predetermined price. The unexpected price changes can lead to impact costs. Order speed of computer trading system is another factor needed to be taken into account. Since the order speed of high frequency trading measures by microseconds or even one-millionth of a second, it demands highly on the computer. Normally, 10 to 20 microsecond's time difference can make a difference. Furthermore, China's high frequency trading system is immature and undeveloped. Almost all of China's exchanges impose restrictions on intraday stock volume for every investor and this restrictive provision also stops the development of high frequency trading in Chinese market. Nonetheless, it still can be believed that fuzzy logic momentum analysis system works better than standard volume based system. In the future research, these factors mentioned above need to be considered and perfect fuzzy logic momentum analysis system further.
VII. References
1. Aldridge, I. (2009). High-frequency trading: a practical guide to algorithmic strategies and trading systems, John Wiley & Sons, Inc.
2. Dourra, H. and Siy, P. (2002). Investment using technical analysis and fuzzy logic. Fuzzy Sets and Systems, Vol. 127 (2002), pp. 221-240.
3. Hellmann, M. Fuzzy logic introduction.
4. Jantzen, J. (1998). Tutorial on fuzzy logic, Technical University of Denmark, Department of Automation.
5. Jang, R. (1993). ANFIS: Adaptive network-based fuzzy inferences system, IEEE Transactions on Systems, Man and cybernetics, Vol. 23 NO.3.
6. MathWorks (2002). Fuzzy logic toolbox for use with MATLAB, MathWorks, Inc.
7. Wikipedia1 (2011). http://en.wikipedia.org/wiki/High-frequency_trading
8. Wikipedia2 (2011). http://en.wikipedia.org/wiki/Matlab
