Genetic Programming in Statistical Arbitrage Philip Saks PhD Seminar  17.10.2007
Contents <ul><li>Introduction </li></ul><ul><li>Genetic Programming </li></ul><ul><li>Clustering of Financial Data </li></...
Introduction <ul><li>To develop an automated framework for trading strategy design, by employing evolutionary computation ...
GP I <ul><li>EC is a concept inspired by the Darwinian survival of the fittest principle – The rationale being, that natur...
GP II <ul><li>GP’s are basically GA’s in which the genome contitutes hierachical computer programs </li></ul><ul><li>Using...
Clustering of Financial Data
Data  <ul><li>Hourly VWAP prices and volume for banking stocks within the Euro Stoxx Universe, covering the period from 01...
Framework <ul><li>Evolve trading rules with binary decisions </li></ul><ul><li>We consider the classical single tree setup...
Results <ul><li>Trading on VWAP, assuming 1bp market impact </li></ul>
Sensitivity Analysis
Stress Testing I
Turnover Analysis
Transaction Cost Implications
Conclusion  <ul><li>It is possible to discover profitable arbitrage trading rules on the Euro Stoxx banking sector. </li><...
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Philip Genetic Programming In Statistical Arbitrage

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Philip Genetic Programming In Statistical Arbitrage

  1. 1. Genetic Programming in Statistical Arbitrage Philip Saks PhD Seminar 17.10.2007
  2. 2. Contents <ul><li>Introduction </li></ul><ul><li>Genetic Programming </li></ul><ul><li>Clustering of Financial Data </li></ul><ul><li>Data </li></ul><ul><li>Framework </li></ul><ul><li>Results </li></ul><ul><li>Conclusion </li></ul>
  3. 3. Introduction <ul><li>To develop an automated framework for trading strategy design, by employing evolutionary computation in conjunction with other machine learning paradigms </li></ul><ul><li>The present framework utilize genetic programming </li></ul><ul><li>Much of the existing financial forecasting using GP has focused on high-frequency FX [Jonsson, 1997][Dempster and Jones, 2001][Bhattacharyya et al, 2002] and the general consencus is that there is predictability, and excess return is achievable in the pressence of transaction costs </li></ul><ul><li>For stocks, the results are mixed [Allen and Karjalainen, 1999] do not significantly out-perform the buy-and-hold on S&P500 daily data, but [Becker and Sheshadri, 2003] do on monthly. </li></ul>
  4. 4. GP I <ul><li>EC is a concept inspired by the Darwinian survival of the fittest principle – The rationale being, that natural evolution has proved succesfull in solving a wide range of problems throughout time, hence an algorithm that mimics this behavior, might solve a wide range of artificial problems </li></ul><ul><li>The concept was pioneered by Holland (1975) in the form of Genetic Algorithms (GA) </li></ul><ul><li>A GA is essentially a population based search method, where each candidate solution is incoded in a fixed length binary string. </li></ul><ul><li>The population evolves, via mainly three operators, selection, reproduction and mutation. </li></ul><ul><li>The selection process is based on the survival of the fittest principle. </li></ul>
  5. 5. GP II <ul><li>GP’s are basically GA’s in which the genome contitutes hierachical computer programs </li></ul><ul><li>Using this representation, we can solve problems in a wide range of fields such as, symbolic or ordinary regression, classification, optimal control theory etc. since each of these areas “can be viewed as requiring discovery of a computer program that produces some desired output for particular inputs” (Koza, 1992) </li></ul><ul><li>Tree representation of programs, function & terminal Set </li></ul><ul><li>Evolutionary operators: selection, cross-over & mutation </li></ul>
  6. 6. Clustering of Financial Data
  7. 7. Data <ul><li>Hourly VWAP prices and volume for banking stocks within the Euro Stoxx Universe, covering the period from 01-Apr-2003 to 29-Jun-2007 (8648 oberservations). </li></ul>
  8. 8. Framework <ul><li>Evolve trading rules with binary decisions </li></ul><ul><li>We consider the classical single tree setup, but also a dual tree framework, where buy and sell rules are co-evolved. </li></ul><ul><li>The training set comprises 6000 samples, while the remaining 2647 are used for out-of-sample testing </li></ul><ul><li>10 runs are performed for each experiment. </li></ul>
  9. 9. Results <ul><li>Trading on VWAP, assuming 1bp market impact </li></ul>
  10. 10. Sensitivity Analysis
  11. 11. Stress Testing I
  12. 12. Turnover Analysis
  13. 13. Transaction Cost Implications
  14. 14. Conclusion <ul><li>It is possible to discover profitable arbitrage trading rules on the Euro Stoxx banking sector. </li></ul><ul><li>A cooperative co-evolution of buy and sell rules are beneficial to the classical single tree structure. </li></ul><ul><li>Optimizing in the pressence of transaction costs makes a difference – There should be correspondence between assumption and application for optimal performance. </li></ul>

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