Index Trading Using Grammatical Evolution

8/6/2019 Index Trading Using Grammatical Evolution

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INDEXTRADING USING

GRAMMATICAL EVOLUTION

Munagala Venkatesh

200701237

Supervisor

Prof. Samaresh Chatterji1


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INDEX

Problem definition

Introduction Technical indicators

Genetic algorithm

Mapping process Fitness function

Results

AnalysisAcknowledgement

References2


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PROBLEM DEFINITION

Implementing the index trading model

developed by Dr. Anthony Brabazon.

Improving the performance of the

system by changing the genetic

parameters.

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INTRODUCTION

Index trading is an example of program trading

where a fixed amount of money is invested in themarket index (or fixed amount of investment is

sold out) based on the trading signal buy (or

sell) generated by the trading system.

The trading system uses technical indicators for

generating the trading signal.

Enumeratively trying all possible combinations is

very difficult.4


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TECHNICAL INDICATORS

Moving average:They compare current price with the moving average of theprice.

Current price > moving average increasing trend

Ma(int, day)

Momentum:price(t) / price(t-x)

Reduction in upward momentum market over brought

Reduction in downward momentum market over sold5


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GENETIC ALGORITHM

Initially N candidate solutions encoded in thebinary strings are selected for first generation.

Fitness is calculated for each of them usingfitness function defined for that specific problem.

Select a pair of binary strings from the currentpopulation, the probability of selection being anincrease function of fitness.

With probability pc crossover the pair to form twooffsprings and with probability pm mutateoffsprings at each position and finally add themto the new population. 6


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GENETIC ALGORITHM (CONTINUED)

Repeat the previous two steps until the size of

new population becomes N.

Now replace the current population with new

population for the next generation of algorithm.

After several generations best solution is evolved.

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GENETIC ALGORITHM (CONTINUED)

Selection:

1.) Roulette wheel2.) Tournament selection

Replacement1.) General

2.) Steady state

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MAPPING PROCESS

::=

::= (,) | (,) |

|

::= f_and | f_or

::= greater | lesser

::= + | - | *

::= | ma( , day ) | momentum ( , day) |trb ( , day)

::= 1 | 2 | 3 | 4 | 5 | 10

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MAPPING PROCESS (CONTINUED)

11100010111000011101001010010100101010..

Codons are generated for the binary string taking 8bits at a time and converting to an integer.

226 225 213 83 .

::= greater | lesser

Two possibilities, so we use the formula

rule = c mod r; c=codon value, r= no. of possibilities.In our example rule = c mod 2

if rule = 0, we choosegreater

if rule = 1, we choose lesser10


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Consider the following codon string

225 84 150 34 167 45

Start with the start symbol

::= , only one possibility225 mod1=0

::= (,) | (,) |

| 11


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There are 4 possibilities. Take the nest codon 85

85 mod4 = 1, so choose second possibility (,)

With the next codon 150, use production rule for the

non-terminal from left-side.

In this way the codon string can be mapped to a

solution like

f_and ( lesser ( trb ( 4 , day ) , trb ( 3 , day ) ) , lesser (

momentum ( 1 , day ) , momentum ( 3 , day ) ) )12


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FITNESS FUNCTION

The fitness is calculated over the FTSE data set

of 440 days.

Using the solution formed from the grammar

trading signal (buy or sell ) is generated.

According to it $1000 is invested in the market or

shares for $1000 are sold out.

The total profit gained over 440 days is assignedas fitness to the solution.

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RESULTS

Replacement: Steady

stateSelection:Roulette wheel

wheel

Replacement: General

Selection: Roulettewheel

Training period

(days)

Profit

(US$)

Train (75 to 440) 4834

Test 1 (440 to 805) 5968

Test 2 (805 to 1170) -2466

Test 3 (1170 to 1535) 2805

Test 4 (1535 to 1900) 866

Training period

(days)

Profit

(US$)

Train (75 to 440) 2838

Test 1 (440 to 805) 4988

Test 2 (805 to 1170) 279

Test 3 (1170 to 1535) 2325

Test 4 (1535 to 1900) 81214


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RESULTS (CONTINUED)

Replacement: Steady

stateSelection: Tournament

Replacement: General

Selection: Tournament

Training period

(days)

Profit

(US$)

Train (75 to 440) 4921

Test 1 (440 to 805) 5182

Test 2 (805 to 1170) 1666

Test 3 (1170 to 1535) 2238

Test 4 (1535 to 1900) 1356

Training period

(days)

Profit

(US$)

Train (75 to 440) 4584

Test 1 (440 to 805) 5780

Test 2 (805 to 1170) -2225

Test 3 (1170 to 1535) 2746

Test 4 (1535 to 1900) 97115


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ANALYSIS

Results for the model

developed by AnthonyBrabazon.

Selection: Steady state

Replacement:Tournament

Training period

(days)

Profit

(US$)

Train (75 to 440) 3071

Test 1 (440 to 805) 5244

Test 2 (805 to 1170) -1376

Test 3 (1170 to 1535) 1979

Test 4 (1535 to 1900) 1568

Training period

(days)

Profit

(US$)

Train (75 to 440) 4921

Test 1 (440 to 805) 5182

Test 2 (805 to 1170) 1666

Test 3 (1170 to 1535) 2238

Test 4 (1535 to 1900) 135616


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CONCLUSION

More profit ($15363) is obtained in case 3 in whichselection method and replacement strategy is tournament

and steady state respectively.

Best individuals of past generations are retained in futuregenerations as we used steady state replacement and atthe same time using tournament selection there is a

possibility of generating better children with worst parents.

Thus the results justified the efficiency of genetic algorithmparameters.

The time taken for each run of the genetic algorithm is lessthan a minute and sometimes it is very fast also, so we canmany solve many np-hard problems which requiresexponential time using the evolutionary programmingapproach.

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ACKNOWLEDGMENT

I would like to thank Prof.Samaresh Chatterji for

his proper guidance and who was always there tohelp me whenever I faced the problem.

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REFERENCES

NYSE(2005). Market Information-Quick reference sheet,http://www.nyse.com

Anthony Brabazon, Michael ONeill (2006) Biologically inspiredalgorithms for financial modeling. pp. 183-192 ISBN 3-540-26252-0

Melanie Mitchell (1996), An Introduction to Genetic algorithms, pp.1-15, ISBN-81-203-1358-5.

Murphy, John J. (1999). Technical Analysis of the Financial markets,New York: New York institute of finance.

Brock, W., Lakonishok, J. and LeBaron B. (1992). Simple technical

trading rules and the stochastic properties of stock returns, Journalof finance, 47(5):1731-1764.

Glassman, R. (1973). Persistence and loose coupling in living systems,Behavioral science18:83-98. 19


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THANK YOU

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Index Trading Using Grammatical Evolution

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