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Genetic learning as an explanation of stylized facts of foreign exchange markets

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  • Lux, Thomas
  • Schornstein, Sascha

Abstract

This paper revisits the Kareken-Wallace model of exchange rate formation in a two-country overlapping generations world. Following the seminal paper by Arifovic (Journal of Political Economy, 104, 1996, 510-541) we investigate a dynamic version of the model in which agents' decision rules are updated using genetic algorithms. Our main interest is in whether the equilibrium dynamics resulting from this learning process helps to explain the main stylized facts of free-floating exchange rates (unit roots in levels together with fat tails in returns and volatility clustering). Our time series analysis of simulated data indicates that for particular parameterizations, the characteristics of the exchange rate dynamics are, in fact, very similar to those of empirical data. The similarity appears to be quite insensitive with respect to some of the ingredients of the GA algorithm (i.e. utilitybased versus rank-based or tournament selection, binary or real coding). However, appearance or not of realistic time series characteristics depends crucially on the mutation probability (which should be low) and the number of agents (not more than about 1000). With a larger population, this collective learning dynamics looses its realistic appearance and instead exhibits regular periodic oscillations of the agents' choice variables. -- Dieses Papier betrachtet das Kareken-Wallace-Modell für die Wechselkursbildung in einer Welt mit 2 Ländern und sich überlappenden Generationen. In der Nachfolge des zukunftsweisenden Papiers von Arifovic (1996) untersuchen wir eine dynamische Version des Modells bei dem die Entscheidungsregeln mithilfe genetischer Algorithmen jeweils aktualisiert werden. Unser Hauptinteresse geht dahin, herauszufinden, ob die Gleichgewichtsdynamik, die aus diesem Lernprozess resultiert, dabei helfen kann, die wichtigsten stilisierten Fakten von flexiblen Wechselkursen zu erklären (Einheitswurzeln bei den Niveaus mit dicken Enden der Ertragsverteilung und Klumpenbildung bei den Volatilitäten). Unsere Analyse simulierter Daten weist darauf hin, dass für bestimmte Parametrisierungen der Charakter der Wechselkursdynamik tatsächlich dem von empirischen Daten sehr ähnlich ist. Die Ähnlichkeit scheint sehr wenig von speziellen Eigenschaften des gewählten GA-Algorithmus abzuhängen (z. B. nutzenbasiert versus rangbasiert, binäre oder reale Kodierung). Dagegen ist die Mutationswahrscheinlichkeit (die niedrig sein sollte) und die Anzahl der Agenten (die nicht größer als 1000 sein sollte) wichtig. Mit mehr Teilnehmern verliert die kollektive Lerndynamik ihr realistisches Aussehen und es kommt zu regelmäßigen periodischen Schwankungen bei den Variablen, die die Agenten auswählen.

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Bibliographic Info

Paper provided by Deutsche Bundesbank, Research Centre in its series Discussion Paper Series 1: Economic Studies with number 2002,29.

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Date of creation: 2002
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Handle: RePEc:zbw:bubdp1:4194

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Related research

Keywords: Learning; Genetic algorithms; Exchange rate dynamics;

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References

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  1. Meese, Richard A. & Rogoff, Kenneth, 1983. "Empirical exchange rate models of the seventies : Do they fit out of sample?," Journal of International Economics, Elsevier, vol. 14(1-2), pages 3-24, February.
  2. Shu-Heng Chen & Thomas Lux & Michele Marchesi, 1999. "Testing for Non-Linear Structure in an Artificial Financial Market," Discussion Paper Serie B 447, University of Bonn, Germany.
  3. Giulia Iori, 1999. "A microsimulation of traders activity in the stock market: the role of heterogeneity, agents' interactions and trade frictions," Finance 9905005, EconWPA.
  4. Egenter, E. & Lux, T. & Stauffer, D., 1999. "Finite-size effects in Monte Carlo simulations of two stock market models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 268(1), pages 250-256.
  5. repec:att:wimass:9530 is not listed on IDEAS
  6. Hens, Thorsten & Schenk-Hoppe, Klaus Reiner, 2005. "Evolutionary stability of portfolio rules in incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 43-66, February.
  7. Arifovic, Jasmina, 1996. "The Behavior of the Exchange Rate in the Genetic Algorithm and Experimental Economies," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 510-41, June.
  8. Damien Challet & Matteo Marsili, 2002. "Criticality and finite size effects in a simple realistic model of stock market," Papers cond-mat/0210549, arXiv.org, revised Dec 2002.
  9. Gaunersdorfer, A. & Hommes, C.H., 2000. "A Nonlinear Structural Model for Volatility Clustering," CeNDEF Working Papers 00-02, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  10. Brock, W.A. & Hommes, C.H., 1996. "A Rational Route to Randomness," Working papers 9530r, Wisconsin Madison - Social Systems.
  11. Chia-Hsuan Yeh, Shu-Heng Chen, 2001. "The Influence of Market Size in an Artificial Stock Market: The Approach Based on Genetic Programming," Computing in Economics and Finance 2001 74, Society for Computational Economics.
  12. Carl Chiarella & Xue-Zhong He, 2001. "Asset Price and Wealth Dynamics Under Heterogeneous Expectations," Research Paper Series 56, Quantitative Finance Research Centre, University of Technology, Sydney.
  13. Lux, T. & M. Marchesi, . "Volatility Clustering in Financial Markets: A Micro-Simulation of Interacting Agents," Discussion Paper Serie B 437, University of Bonn, Germany, revised Jul 1998.
  14. Arifovic, Jasmina & Gencay, Ramazan, 2000. "Statistical properties of genetic learning in a model of exchange rate," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 981-1005, June.
  15. John F. O. Bilson, 1980. "The "Speculative Efficiency" Hypothesis," NBER Working Papers 0474, National Bureau of Economic Research, Inc.
  16. Brock,W.A. & Hommes,C.H., 2001. "Evolutionary dynamics in financial markets with many trader types," Working papers 7, Wisconsin Madison - Social Systems.
  17. Gilles Teyssière & Alan Kirman, 2001. "Microeconomic Models for Long-Memory in the Volatility of Financial Time Series," CeNDEF Workshop Papers, January 2001 5A.4, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  18. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, October.
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