Abstract- The modeling of fiscal systems continues to keep great involvement for non lone research workers but besides investors and policymakers. Many of the features of these systems, nevertheless, can non be adequately captured by traditional fiscal modeling attacks. Fiscal systems are complex, nonlinear, dynamically altering systems in which it is frequently hard to place mutualist variables and their values. Financial securities firm is concerned with put to deathing orders of purchasing and merchandising of certain sums of portions at the best possible monetary value. Many mathematical and algorithmic systems have been developed for this undertaking, nevertheless they can non look

Keywords ; Finacial securities firm ; fuzzed logic ; high frequence trading.

Introduction

It is good known that a chief insufficiency of much economic theory is that it postulates exact functional relationships between variables. On the other manus in fiscal clip series analysis, information points seldom lie precisely on consecutive lines or smooth maps. [ 7 ] suggests that trying to suit these nonlinear phenomena will present an unacceptable degree of instability in theoretical accounts.

As a consequence of this intractableness, research workers and investors are turning to unreal intelligence techniques to better inform their theoretical accounts, making determination support systems that can assist a human user better understand complex fiscal systems such as stock markets. Artificial intelligence systems in portfolio choice have been shown to hold a public presentation border over the human portfolio director and recent research suggests that attacks that incorporate unreal intelligence techniques are besides likely to surpass classical fiscal theoretical accounts [ 4 ] .

Artificial intelligence attacks have late been normally adopted in fiscal modeling. Traditionally, stock market calculating methodological analysiss have been based on either cardinal or proficient analysis. Cardinal analysis efforts to find the intrinsic value of stocks based on extended macroeconomic informations, whereas proficient analysis relies on analyzing market activity, peculiarly historic monetary values and volume. Whilst there is much back uping research for both schemes in fiscal theory we focus on systems utilizing proficient methodological analysis as the subjective and complex nature of cardinal analysis means it has, to day of the month, received small attending in unreal intelligence research.

Fuzzy logic was foremost introduced by [ 6 ] . It is a signifier of multivalent logic which, whilst retaining the deductive construction of classical symbolic logic, includes the construct of grade of truth. Rather than being either true or false, as in binary logic, statements in fuzzed logic have a rank map which defines a fuzzy set ( as opposed to a chip set in conventional set theory ) . Fuzzy logic is hence an ideal attack to jobs that require a representation that can cover with estimates, uncertainness and deficient information and it has been applied to spheres every bit diverse as pattern acknowledgment [ 10 ] , railroad control systems [ 2 ] and computing machine game design [ 11 ] . The regulation base and illation engine of a fuzzed system is comparable to that of the cognition base of an expert system. The application of fuzzed set theory in economic science was foremost presented by [ 12 ] and has since received much attending [ 3 ]

Time series theoretical accounts were

This paper is outlined as follows. In subdivision II we give a general overview about fuzzed logic illation systems. Section III introduces the fuzzed logic impulse analysis system ( FL-MAS ) . Section IV explains the methodological analysis of utilizing FL-MAS for securities firm. Section V provides a public presentation analysis of the system. Finally, reasoning comments are given in Section VI.

Fuzzy illation Systems

Many types of fuzzed illation systems have been proposed in literature, nevertheless, in the execution of an ANFIS for fiscal anticipations and appraisal, the most suited theoretical account is the Sugeno theoretical account, which uses if-then-rules to bring forth an end product for each regulation which is the additive combination of the input variables plus a changeless term, and the concluding end product is the leaden norm of each regulation ‘s end product. The regulation base in the Sugeno Model, has regulations of the signifier:

If X is A1 and Y is B1 so f1 = p1* x + q1* y + r1

If X is A2 and Y is B2 so f2 = p2 * x + q2 * y + r2

( 1 ) where X & A ; Y are predefined rank maps, Ai and Bi are rank values, and pi, chi, and Rhode Island are the attendant parametric quantities that are updated in the forward base on balls in the acquisition algorithm. When we calculate the equation of “ First order Sugeno ” the grade of rank variable of X1 in rank map of Ai is multiplied by the grade of rank variable of X2 in rank map Bi and the merchandise is deemed a first Liner Regression Weight ( Wi ) . Finally the leaden mean F1 and F2 is deemed the concluding end product ( Z ) which is calculated as follows:

A fuzzed illation systems shown in Fig. 1 is a regulation based fuzzy system that can be seen as an associatory memory and is made of five constituents ; regulation base which consists of the fuzzed if-then regulations, the informations base which defines rank maps of the fuzzed sets used in the fuzzy regulations, the determination devising unit which is the nucleus unit and is besides known as the illation engine, the fuzzification interface which transforms chip inputs into grades of fiting lingual values, and eventually the defuzzification interface which transforms fuzzed consequences into sharp end product [ 13 ] .

Fuzzy Logic Momentum Analysis System

Making a fuzzed illation system to observe impulse is a complex undertaking. The designation of assorted market conditions has been a subject topic to assorted theories [ 14 ] and suggestions. This paper proposes a fuzzed illation system which categorises the market conditions into 7 classs based on monetary value motion, and will utilize the current volume to find the engagement rates ( PR ) of the trading system each clip.

Fuzzy Inference

## Momentum Analysis

The first measure in planing the Fuzzy Logic Momentum Analysis System, FL-MAS, is specifying the market conditions that the fuzzy system has to place. In this paper we use the following 7 market conditions to cover all possible motions of the monetary value series:

Beat uping

Strong up

Slightly up

Average

Slightly down

Strong down

Crashing

These conditions are considered as lingual values for the fuzzy logic system, and will be used to find the current province of the monetary value formation and its impulse. As impulse is built up, the system looks at the old x sum of ticks and performs an illation process by adding all the motions of the current monetary value to the old monetary value to find whether the general tendency has been up or down after ten points. In other words, impulse is detected by the followers:

where is the current monetary value, is the old monetary value, and is a fluctuating counter which goes up or down harmonizing to the motion of the monetary value. whenever monetary value goes up it adds 1, when the monetary value goes down it subtracts 1, therefore this can be used in placing market conditions for x sum of points, where if the market is traveling strongly upwards, it will be detected by holding more 1s than -1 or 0s. This can be explained in the undermentioned equation:

( 2 )

where is the period that we want to observe the impulse for. For illustration, if we want to observe the impulse of the last 100 ticks, we add all the up, down fluctuations and so feed the ensuing figure to the fuzzy system which would lie someplace in the rank maps shown in Fig. 2.

Membership maps for the lingual variable of market conditions

The same process is applied for ciphering the lingual variable volatility, where the lingual values are as follows:

Very fast

Fast

Medium

Decelerate

Very slow

The fuzzy logic system takes both market impulse and volatility in consideration ; it generates the regulations, and eventually takes a determination based upon the sum of market engagement.

## The Data

Experiments in this paper have been carried out on high frequence tick-data of both Vodafone Group plc ( VOD ) and Nokia Corporation ( NOK ) . For both stocks, 2 months of high frequence tick-data between 2nd Jan 2009 and 27th Feb 2009 has been obtained, and split into 30 subdivisions each. This was done in order to avoid any car correlativity between the monetary values. In other words, the fuzzy logic system gets the first batch of informations, performs all the actions of bargains or sells on it, so the same is process repeated utilizing the criterion volume based system, eventually comparing the public presentation of both systems. Once the observation is obtained, the system skips about 10000 ticks and performs the same operations once more, for 30 times, each clip observing the public presentation of both systems. It has to be mentioned that 2 months of high frequence tick informations is a significantly big sum of informations, taking in consideration that for each loop the system takes the analysis of the impulse of the past 100 ticks. Fig. 3 shows how the information is split after each simulation in order to avoid any possible similarities or autocorrelation in the monetary value.

FL-MAS for securities firm

tick informations

discarded

tick informations

High frequence tick by tick informations

Sim 1

Sim 2

Sim N

The chief aim of the Fuzzy Logic Momentum Analysis System ( FL-MAS ) implemented in this paper is to surpass the industry criterion volume system, that has been used by securities firm houses to put to death big orders of purchasing or selling a certain stock. Many systems have used quantum modeling and analysis to find the assorted engagement rates ( PR ) , nevertheless they normally fail to surpass the criterion volume system in the long term [ 15 ] . This paper uses FL-MAS presented in subdivision 3, to find the PR in the market harmonizing to the current impulse. In other words, if we are on a bargain order, we would prefer to increase the PR ( figure of portions bought at that clip ) , when the monetary value is low, and diminish the engagement when the monetary value is high.

Tick informations splitting mechanism

## Standard Volume System ( SVS )

A standard securities firm mechanism for put to deathing big orders is a simple volume based system, which parses the volume being traded, whenever a certain sum of portions ( a threshold ) have been traded, the system would purchase or sell ( depending on the order ) a certain per centum of that. In other words, if there is an order to merchandise 1 million portions of a certain stock. The threshold would be for e.g. 10,000 portions, and whenever 10,000 portions have been traded, if the PR is set to 25 % , the system would purchase or sell 25 % of the mean volume.

( 3 )

where N is the figure of operations required to make the mark order for illustration 1 million portions, % is a fixed PR, for illustration, 25 % whenever the threshold is exceeded. The above system has proved to be efficient and is being adopted by many securities firm houses around the universe. The purpose of this paper, is to turn out that FL-MAS outperforms this type of system on the long tally.

## FL-MAS

The thought here is to utilize the fuzzy logic impulse analysis system described in subdivision 3, to place what market status we are presently shacking in. This will let us to change the PR ( % ) . This provides an advantage, since the system can merchandise sharply when the status is at an extreme. It would besides understate its trading when the status is at another extreme. In other words, if we are selling million portions, the system will do a trade whenever the threshold of volume has been exceeded. However if the current market status indicates that the monetary value is really high or beat uping so we know that this is a good clip to sell a batch of portions, for illustration 40 % of the current volume. The same thing applies for when the impulse indicates that the monetary value is strong down which means that the system should sell less sums of volume at this low monetary value, for illustration 15 % . The contrary mechanism applies for purchasing portions. When the market is crashing, this is a good index that we should purchase a big ball of volume ( 40 % ) , and when the monetary value is at an mean point, this means that it would act like the SVS system i.e. purchasing 25 % of Volume. This is shown in Table 1.

Engagement rates for buy side and the sell side of FL-MAS

Market Condition

Buying Praseodymium

Selling Praseodymium

Beat uping

10 %

40 %

Strong up

15 %

35 %

Slightly up

20 %

30 %

Average

25 %

25 %

Slightly down

30 %

20 %

Strong down

35 %

15 %

Crashing

40 %

10 %

## Performance Measures

After implementing both SVS and FL-MAS, the standards at which both systems will be compared against each other will be the outperformance of FL-MAS on the SVS in footing points. TheA footing point is a unit of step used frequently to depict the per centum at which a alteration in the value or rate of a fiscal instrument has occurred. One footing point is a1/100th of a per centum orA 0.01 % . It is besides tantamount to 0.0001 in denary signifier.

To cipher the betterment ( elf ) for the buy side in footing points we use the undermentioned expression:

## iˆ?iˆ?iˆ©

For the Sell Side the betterment in footing points is:

## iˆ?iˆµiˆ©

Where is the entire cost of purchasing x sum of portions utilizing FL-MAS, and is the entire cost of purchasing the same figure of portions utilizing the traditional SVS.

Consequences

This subdivision displays the consequences of utilizing both FL-MAS and SVS to purchase 1million portions of VOD and NOK. For each symbol 30 simulations have been carried on the tick-data set described in subdivision 3. The information has been split as described in order to avoid any autocorrelations, both systems have been run and tested on the same information sets. Table 2 displays the cost at each simulation for purchasing 1million portions of NOK utilizing both systems. The mean monetary value of the whole set is besides displayed, and eventually the betterment of FL-MAS against SVS is displayed. This betterment rate can be either positive ; when FL-MAS has outperformed SVS or negative ; when FL-MAS was outperformed by SVS.

Table 3 provides a full analysis of Table 2, by demoing clearly the mean outperformance rate of purchasing 1million portions of NOK utilizing FL-MAS, which turns out to be a positive of 2.98 footing points, which means that on mean utilizing FL-MAS we save about 3 footing points whenever we buy 1 million portion of NOK. Table 3 besides displays the consequences of implementing both systems to purchase 1 million portions of VOD. These consequences for VOD ( besides displayed on Fig.4 ) show a much higher mean of around 12.5 footing points. Experiments have been performed once more by reshuffling the information sets utilizing the informations slots that have non been used before, and the observations were really similar to these consequences. Hence another measuring mechanism was to detect the median of the consequences. The median is described as the figure dividing the higher half of a sample or distribution from the lower half. Both Medians for NOK, and VOD were positive, bespeaking that on mean FL-MAS outperforms SVS for all the purchasing Simulations.

Comparing the public presentation of FL-MAS against SVS for purchasing 1M portions of NOK

Average

Monetary value

Cost of purchasing

1m NOK Shares

utilizing FLMAS

Cost of purchasing

1m NOK Shares

utilizing SVS

Improvement

in footing points

11.55

11278964

11285761

6.02

12.19

11581642

11572708

-7.72

11.57

11904468

11910571

5.12

11.12

11610312

11581174

-25.16

11.45

11076799

11087759

9.88

11.36

11456338

11452293

-3.53

11.03

11390049

11404634

12.79

10.89

10947120

10956223

8.31

10.45

10923870

10950576

24.39

10.31

10373596

10377899

4.15

10.63

10354815

10367941

12.66

10.78

10655795

10644194

-10.90

10.70

10816236

10814437

-1.66

10.45

10723627

10737409

12.84

10.24

10281461

10286957

5.34

10.48

10214443

10205979

-8.29

9.67

10553155

10547707

-5.17

9.67

9581014

9602197

22.06

9.40

9754339

9740190

-14.53

9.22

9521736

9544895

24.26

9.10

9282640

9280416

-2.40

9.38

9135088

9149560

15.82

9.27

9434147

9457587

24.78

9.42

9262702

9272236

10.28

9.77

9439104

9430047

-9.60

9.87

9807817

9799844

-8.14

9.49

9880881

9885421

4.59

9.58

9585207

9580119

-5.31

9.48

9619778

9624263

4.66

9.40

9556780

9555829

-1.00

9.67

9350444

9359424

9.59

9.98

9724834

9707290

-18.07

9.94

9869580

9869177

-0.41

Analysis of consequences of purchasing 1m portions of NOK and VOD

Mean ( elf )

Median ( elf )

Entire ( elf )

Buying NOK

2.98

4.63

101.18

Buying VOD

12.48

1.58

374.53

Besides the entire betterment of both is really high indicating that for both the 30 simulations, a 101.18 footing points was saved utilizing FL-MAS on NOK, and a 374.53 on VOD.

Buying 1m portions of VOD

Similarly, the sell side is displayed in Table 4, and analysed in Table 5. Similar to the bargain side, all simulations and experiments utilizing FL-MAS and SVS, have displayed that on mean FL-MAS has proved to be the better system, and therefore would increase the profitableness of a fiscal securities firm house that executes multiple big orders. Fig. 5 displays the merchandising of 1m portions of VOD.

Comparing the public presentation of FL-MAS against SVS for selling 1M portions of VOD

Average

Monetary value

Cost of selling

1m VOD Shares

utilizing FLMAS

Cost of selling

1m VOD

Shares utilizing SVS

Improvement

in footing points

139.75

138379831

138304137

5.47

142.10

141880579

141466276

29.20

147.30

145752861

145974583

-15.21

145.70

147127925

147242618

-7.80

144.50

145284236

145840646

-38.30

148.30

141887321

141926909

-2.79

138.30

138593022

138540789

3.77

137.60

138159371

138119542

2.88

138.45

137192635

137152512

2.92

138.80

136243869

137297036

-77.30

138.70

138854269

138889050

-2.50

135.95

134818894

134622571

14.56

133.85

135551066

135198498

26.01

136.50

133744440

133824812

-6.01

135.55

136450408

136384280

4.85

139.50

136381824

136248448

9.78

138.30

138364382

138217262

10.63

136.85

136263730

136277519

-1.01

134.20

133894601

133855738

2.90

134.56

133894289

132534941

101.52

127.10

129477007

129129593

26.83

128.90

127159502

127174918

-1.21

130.85

129889373

129821846

5.20

135.50

130203793

130019981

14.12

136.85

135468629

135441956

1.97

136.45

136622702

136595289

2.01

138.05

136719313

136746751

-2.01

136.65

134943043

135082269

-10.32

132.15

133857223

134159108

-22.55

Analysis of consequences of Selling 1m portions of NOK and VOD

Mean ( elf )

Median ( elf )

Entire ( elf )

Selling NOK

1.6812

2.9291

57.16

Selling VOD

2.73

2.46

81.83

Selling 1m portions of VOD

Decision

The job of order executing is a really complicated one. To be able to supply the best monetary value, an executing system has to dynamically alter the engagement rates at each case in order to provide for monetary value alterations, which are driven by impulse and volatility. This paper has introduced a system that makes usage of fuzzed logic, in order to ground out the current market status which is produced by the accretion of impulse. FL-MAS is a fuzzed logic impulse analysis system that outperforms the traditional systems used in industry which are frequently based on put to deathing orders based on the leaden norm of the current volume. Consequences of the enforced system have been displayed and compared against the traditional system. The system proves that on norm it increases profitableness on orders both on the bargain and sell sides. Further work and research has to be done to optimize the public presentation of the system. This could either include the usage of a familial algorithm to optimize the rank maps or the usage of Adaptive Neuro Fuzzy systems which would bring forth all the possible regulations for the system.