Skip to main content
SpringerLink
Log in
Book cover

Long Memory in Economics pp 265–288Cite as

A Nonlinear Structural Model for Volatility Clustering

  • Chapter

Summary

A simple nonlinear structural model of endogenous belief heterogeneity is proposed. News about fundamentals is an IID random process, but nevertheless volatility clustering occurs as an endogenous phenomenon caused by the interaction between different types of traders, fundamentalists and technical analysts. The belief types are driven by adaptive, evolutionary dynamics according to the success of the prediction strategies as measured by accumulated realized profits, conditioned upon price deviations from the rational expectations fundamental price. Asset prices switch irregularly between two different regimes — periods of small price fluctuations and periods of large price changes triggered by random news and reinforced by technical trading — thus, creating time varying volatility similar to that observed in real financial data.

Earlier versions of this paper were presented at the 27th annual meeting of the EFA, August 23–26, 2000, London Business School, the International Workshop on Financial Statistics, July 5–8, 1999, University of Hong Kong, the Workshop on Expectational and Learning Dynamics in Financial Markets, University of Technology, Sydney, December 13–14, 1999, the Workshop on Economic Dynamics, January 13–15, 2000, University of Amsterdam, and the workshop Beyond Efficiency and Equilibrium, May 18–20, 2000 at the Santa Fe Institute. We thank participants of all workshops for stimulating discussions. Special thanks are due to Arnoud Boot, Peter Boswijk, Buz Brock, Carl Chiarella, Dee Dechert, Engelbert Dockner, Doyne Farmer, Gerwin Griffioen, Alan Kirman, Blake LeBaron, Thomas Lux, Ulrich Müller, and Josef Zechner. Detailed comments by two anonymous referees have led to several improvements. We also would like to thank Roy van der Weide and Sebastiano Manzan for their assistance with the numerical simulations. This research was supported by the Austrian Science Foundation (FWF) under grant SFB#010 (“Adaptive Information Systems and Modelling in Economics and Management Science.”) and by the Netherlands Organization for Scientific Research (NWO) under an NWO-MaG Pionier grant.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anderson, S., de Palma, A. and Thisse, J. (1993). Discrete Choice Theory of Product Differentiation. MIT Press, Cambridge.

    MATH  Google Scholar 

  2. Arifovic, J. and Gencay, R. (2000). Statistical properties of genetic learning in a model of exchange rate. Journal of Economic Dynamics and Control, 24, 981–1005.

    Article  MATH  Google Scholar 

  3. Arthur, W.B., Holland, J.H., LeBaron, B., Palmer, R. and Taylor, P. (1997). Asset pricing under endogenous expectations in an artificial stock market, in: Arthur, W.B., Durlauf, S.N., and Lane, D.A. (Eds.), The Economy as an Evolving Complex System II. Redwood City, Addison-Wesley, pp. 15–44.

    Google Scholar 

  4. Baillie, R.T., Bollerslev, T. and Mikkelsen, H.O. (1996). Fractionally integrated generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 74, 3–30.

    Article  MATH  MathSciNet  Google Scholar 

  5. Bollerslev, T. (1986). Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics, 31, 307–327.

    Article  MATH  MathSciNet  Google Scholar 

  6. Breidt, F.J., Crato, N. and de Lima, P. (1998). The detection and estimation of long memory in stochastic volatility. Journal of Econometrics, 83, 325–348.

    Article  MATH  MathSciNet  Google Scholar 

  7. Brock, W.A. (1993). Pathways to randomness in the economy: Emergent nonlinearity and chaos in economics and finance. Estudios Económicos, 8, 3–55.

    Google Scholar 

  8. Brock, W.A. (1997). Asset price behavior in complex environments, in: Arthur, W.B., Durlauf, S.N., and Lane, D.A. (Eds.), The Economy as an Evolving Complex System II. Addison-Wesley, Reading, MA, pp. 385–423.

    Google Scholar 

  9. Brock, W.A. and Hommes, C.H. (1997a). A rational route to randomness. Econometrica, 65, 1059–1095.

    Article  MATH  MathSciNet  Google Scholar 

  10. Brock, W.A. and Hommes, C.H. (1997b). Models of complexity in economics and finance, in: Hey, C., Schumacher, J.M., Hanzon, B., and Praagman, C. (Eds.), System Dynamics in Economic and Financial Models. John Wiley & Sons, Chichester, pp. 3–41.

    Google Scholar 

  11. Brock, W.A. and Hommes, C.H. (1998). Heterogeneous beliefs and routes to chaos in a simple asset pricing model. Journal of Economic Dynamics and Control, 22, 1235–74.

    Article  MATH  MathSciNet  Google Scholar 

  12. Chiarella, C. (1992). The dynamics of speculative behaviour. Annals of Operations Research, 37, 101–123.

    Article  MATH  MathSciNet  Google Scholar 

  13. DeGrauwe, P., DeWachter, H. and Embrechts, M. (1993). Exchange rate theory. Chaotic models of foreign exchange markets. Blackwell, Oxford.

    Google Scholar 

  14. DeGrauwe, P. and Grimaldi, M. (2004). Exchange rate puzzles: a tale of switching attractors, Working paper, University of Leuven.

    Google Scholar 

  15. Engle, R.F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50, 987–1007.

    Article  MATH  MathSciNet  Google Scholar 

  16. Farmer, J.D. and Joshi, S. (2002). The price dynamics of common trading strategies. Journal of Economic Behavior & Organization, 49, 149–171.

    Article  Google Scholar 

  17. de Fontnouvelle, P. (2000). Information dynamics in financial markets. Macroeconomic Dynamics, 4, 139–169.

    Article  MATH  Google Scholar 

  18. Frankel, J.A. and Froot, K.A. (1986). Understanding the US Dollar in the Eighties: the Expectations of Chartists and Fundamentalists. Economic Record, Special Issue 1986, 24–38.

    Google Scholar 

  19. Gaunersdorfer, A. (2000). Endogenous fluctuations in a simple asset pricing model with heterogeneous beliefs. Journal of Economic Dynamics and Control, 24, 799–831.

    Article  MATH  Google Scholar 

  20. Gaunersdorfer, A. (2001). Adaptive beliefs and the volatility of asset prices. Central European Journal of Operations Research, 9, 5–30.

    MATH  MathSciNet  Google Scholar 

  21. Gaunersdorfer A. and Hommes C.H. (2000). A Nonlinear Structural Model for Volatility Clustering — Working Paper Version. SFB Working Paper No. 63, University of Vienna and Vienna University of Economics and Business Administration, and CeNDEF Working Paper WP 00-02, University of Amsterdam.

    Google Scholar 

  22. Gaunersdorfer, A., Hommes, C.H. and Wagener, F.O.J. (2003). Bifurcation routes to volatility clustering under evolutionary learning. CeNDEF Working Paper 03-03, University of Amsterdam.

    Google Scholar 

  23. Goetzmann, W. and Massa, M. (2000). Daily momentum and contrarian behavior of index fund investors. Journal of Financial and Quantitative Analysis, forthcoming.

    Google Scholar 

  24. Granger, C.W.J. and Ding, Z. (1996). Varieties of long memory models. Journal of Econometrics, 73, 61–77.

    Article  MATH  MathSciNet  Google Scholar 

  25. Grossman, S. and Stiglitz, J. (1980). On the impossibility of informationally efficient markets. American Economic Review, 70, 393–408.

    Google Scholar 

  26. Harvey C.R. and Siddique A. (2000). Conditional skewness in asset pricing tests. Journal of Finance, 55, 1263–1295.

    Article  Google Scholar 

  27. Hirshleifer, D. (2001). Investor psychology and asset pricing. Journal of Finance, 56, 1533–1597.

    Article  Google Scholar 

  28. Hommes, C.H. (2001). Financial markets as nonlinear adaptive evolutionary systems. Quantitative Finance, 1, 149–167.

    Article  MathSciNet  Google Scholar 

  29. Hommes, C.H. (2002). Modeling the stylized facts in finance through simple nonlinear adaptive systems. Proc. Nat. Ac. Sc., 99, 7221–7228.

    Article  CAS  Google Scholar 

  30. Kirman, A. (1991). Epidemics of opinion and speculative bubbles in financial markets, in: Taylor, M. (Ed.), Money and Financial Markets. Macmillan, London, pp. 354–368.

    Google Scholar 

  31. Kirman, A. (1998). On the nature of gurus. Preprint.

    Google Scholar 

  32. Kirman, A. and Teyssière, G. (2002). Microeconomic models for long memory in the volatility of financial time series. Studies in Nonlinear Dynamics & Econometrics, 5, 281–302.

    Article  MATH  Google Scholar 

  33. Kuznetsov, Y.A. (1998). Elements of Applied Bifurcation Theory (2nd ed.). Springer Verlag, New York.

    MATH  Google Scholar 

  34. Kyle, A.S. (1985). Continuous auctions and insider trading. Econometrica, 53, 1315–1335.

    Article  MATH  Google Scholar 

  35. LeBaron, B., Arthur, W.B. and Palmer, R. (1999). Time series properties of an artificial stock market. Journal of Economic Dynamics and Control, 23, 1487–1516.

    Article  MATH  Google Scholar 

  36. Lo, A.W. and MacKinlay, A.C. (1990). When are contrarian profits due to stock market overreaction? The Review of Financial Studies, 3, 175–205.

    Article  Google Scholar 

  37. Lux, T. (1995). Herd behavior, bubbles and crashes. The Economic Journal, 105, 881–896.

    Article  Google Scholar 

  38. Lux, T. and Marchesi, M. (1999). Scaling and criticality in a stochastic multiagent model of a financial market. Nature, 397, 498–500.

    Article  CAS  ADS  Google Scholar 

  39. Lux, T. and Marchesi, M. (2000). Volatility clustering in financial markets: A microsimulation of interacting agents. International Journal of Theoretical and Applied Finance, 3, 675–702.

    Article  MATH  MathSciNet  Google Scholar 

  40. Mandelbrot, B. (1963). The variation of certain speculative prices. Journal of Business, 36, 394–419.

    Article  Google Scholar 

  41. Mandelbrot, B. (1997). Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. Springer Verlag, New York.

    Google Scholar 

  42. Mandelbrot, B. (1999). A multi-fractal walk down Wall Street. Scientific American, 280,(2) 50–53.

    Article  MathSciNet  Google Scholar 

  43. Manski, C. and McFadden, D. (1981). Structural Analysis of Discrete Data with Econometric Applications. MIT Press, Cambridge.

    MATH  Google Scholar 

  44. Manzan, S. (2003). Essays in Nonlinear Economic Dynamics. Thesis, University of Amsterdam.

    Google Scholar 

  45. Pagan, A. (1996). The econometrics of financial markets, Journal of Empirical Finance, 3, 15–102.

    Article  Google Scholar 

  46. Palis, J. and Takens, F. (1993). Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations. Cambridge University Press, New York.

    MATH  Google Scholar 

  47. Routledge B.R. (1999). Adaptive learning in financial markets. The Review of Financial Studies, 12, 1165–1202.

    Article  Google Scholar 

  48. Shefrin, H. (2000). Beyond Greed and Fear. Understanding Behavioral Finance and the Psychology of Investing. Harvard Business School Press, Boston.

    Google Scholar 

  49. Shleifer, A. (2000). Inefficient Markets. An Introduction to Behavioral Finance. Clarendon Lectures in Economics, Oxford University Press.

    Google Scholar 

  50. Timmermann, A. (1993). How learning in financial markets generates excess volatility and predictability in stock prices. Quarterly Journal of Economics, 108, 1135–1145.

    Article  Google Scholar 

  51. Timmermann, A. (1996). Excess volatility and predictability of stock prices in autoregressive dividend models with learning. Review of Economic Studies, 63, 523–557.

    Article  MATH  Google Scholar 

  52. Woodford, M. (2000). An interview with William A. Brock. Macroeconomic Dynamics, 4, 108–138.

    Article  MATH  Google Scholar 

  53. Youssefmir, M. and Huberman, B.A. (1997). Clustered volatility in multiagent dynamics. Journal of Economic Behavior & Organization, 32, 101–118.

    Article  Google Scholar 

  54. Zeeman, E.C. (1974). On the unstable behaviour of stock exchanges. Journal of Mathematical Economics, 1, 39–49.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Business Studies, University of Vienna, Vienna

    Andrea Gaunersdorfer

  2. Center for Nonlinear Dynamics in Economics and Finance, University of Amsterdam, Amsterdam

    Cars Hommes

Authors
  1. Andrea Gaunersdorfer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cars Hommes
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Laboratoire de Statistique Appliquée et de Modélisation Stochastique (SAMOS), Panthéon Sorbonne, Centre Pierre Mendès, Université Paris 1, 90 rue de Tolbiac, 75634, Paris Cedex 13, France

    Gilles Teyssière

  2. L’Ecole des Hautes Etudes en Sciences Sociales (EHESS), Université Aix-Marseille III, 2 rue de la Charité, 13002, Marseille, France

    Alan P. Kirman

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer Berlin · Heidelberg

About this chapter

Cite this chapter

Gaunersdorfer, A., Hommes, C. (2007). A Nonlinear Structural Model for Volatility Clustering. In: Teyssière, G., Kirman, A.P. (eds) Long Memory in Economics. Springer, Berlin, Heidelberg . https://doi.org/10.1007/978-3-540-34625-8_9

Download citation

Publish with us

Policies and ethics

Search

Navigation