Skip to main content
SpringerLink
Log in

Heterogeneity, nonlinearity and endogenous market volatility

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

This paper aims to contribute to the literature on the explanatory power of behavior models with heterogeneous agents. The authors present a new nonlinear structural stock market model which is a nonlinear deterministic process buffeted by dynamic noise. An exogenous noise is introduced to the model with the assumption of IID normal innovations of the fundamental value in order to investigate how noisy dynamics interacts with deterministic process. The market is composed of two typical trader types: the rational fundamentalists and the boundedly rational traders governed by greed and fear. The interaction between noise and deterministic element determines the evolution process of the system as key parameters are changed. The authors find the model is able to generate time series that exhibit dynamical and statistical properties closely resembling those of the S&P500 index, such as volatility clustering, fat tails (leptokurtosis), autocorrelation in square and absolute return, larger amplitude, crashes and bubbles. The authors also investigate the nonlinear dependence structure in our data. The results indicate that the GARCH-type model cannot completely account for all nonlinearity in our simulated market, which is thus consistent with the results from real markets. It seems that the nonlinear structural model is more powerful to give a satisfied explanation to market behavior than the traditional stochastic approach.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E. C. Zeeman, The unstable behavior of stock exchange, Journal of Mathematical Economics, 1974, (1): 39–49.

  2. A. Kirman, Epidemics of opinion and speculative bubbles in financial markets, chapter 17, M. Taylor (Ed.), Money and Financial Markets, Macmillan, London, 1991.

    Google Scholar 

  3. M. M. Dacorogna, et al., Heterogeneous real-time trading strategies in the foreign exchange market, European Journal of Finance, 1995, (1): 383–403.

  4. J. B. DeLong, et al., Noise trader risk in financial markets, Journal of Political Economy, 1990a, (98): 703–738.

  5. J. B. DeLong, et al., Positive feedback investment strategies and destabilizing rational speculation, Journal of Finance, 1990b, 45: 379–395.

    Article  Google Scholar 

  6. F. A. Wang, Strategic trading, asymmetric information and heterogeneous prior beliefs, Journal of Financial Markets, 1998, (1): 321–352.

  7. G. Iori, A microsimulation of traders activity in the stock market: The role of heterogeneity, agents’ interactions and trade frictions, Journal of Economic Behavior and Organization, 2002, 49(2): 269–285.

    Article  Google Scholar 

  8. C. Chiarella, R. Dieci, and X. Z. He, Heterogeneous expectations and speculative behavior in a dynamic multi-asset framework, Journal of Economic Behavior & Organization, 2007, 62(3): 408–427.

    Article  Google Scholar 

  9. H. Amilon, Estimation of an adaptive stock market model with heterogeneous agents, Journal of Empirical Finance, 2008, (15): 342–362.

  10. L. Y. He, Is price behavior scaling and multiscaling in a dealer market? Perspectives from multiagent based experiments, Computational Economics, 2010, 36(3): 263–282.

    Article  MATH  Google Scholar 

  11. F. Black, Noise, Journal of Finance, 1986, 41: 529–543.

    Article  Google Scholar 

  12. R. H. Thaler, The end of behavioral finance, Financial Analysts Journal, 1999, 55(6): 2–17.

    Article  Google Scholar 

  13. R. J. Shiller, The irrationality of markets, The Journal of Psychology and Financial Markets, 2002, 3(2): 87–93.

    Article  Google Scholar 

  14. W. A. Brock and C. H. Hommes, A rational route to randomness, Econometrica, 1997, 65: 1059–1095.

    Article  MATH  MathSciNet  Google Scholar 

  15. W. A. Brock and C. H. Hommes, Heterogeneous beliefs and routes to chaos in a simple asset pricing model, Journal of Economic Dynamics and Control, 1998, 22: 1235–1274.

    Article  MATH  MathSciNet  Google Scholar 

  16. S. H. Chen, T. Lux, and M. Marchesi, Testing for non-linear structure in an artificial financial market, Journal of Economic Behavior and Organization, 2001, 46(3): 327–342.

    Article  Google Scholar 

  17. A. Gaunersdorfer, Endogenous fluctuations in a simple asset pricing model with heterogeneous agents, Journal of Economic Dynamics and Control, 2000, 24: 799–831.

    Article  MATH  Google Scholar 

  18. T. Lux, Herd behaviour, bubbles and crashes, Economic Journal, 1995, (105): 881–896.

  19. T. Lux, The socio-economic dynamics of speculative markets: Interacting agents, chaos, and the fat tails of returns distributions, Journal of Economic Behavior and Organization, 1998, 33: 143–165.

    Article  Google Scholar 

  20. A. G. Malliaris and J. L. Stein, Methodological issues in asset pricing: Random walk or chaotic dynamics, Journal of Banking and Finance, 1999, 23: 1605–1635.

    Article  Google Scholar 

  21. C. H. Hommes and S. Manzan, Comments on “Testing for nonlinear structure and chaos in economic time series”, Journal of Macroeconomic, 2006, 28: 169–174.

    Article  Google Scholar 

  22. A. Sansonea and G. Garofalo, Asset price dynamics in a financial market with heterogeneous trading strategies and time delays, Physica A, 2007, (382): 247–257.

  23. F. Westerhoff, Greed, fear and stock market dynamics, Physica A, 2004, (343): 635–642.

  24. P. Grassberger and I. Procaccia, Characterization of strange attractors, Physical Review Letters, 1983, (50): 346–349.

  25. W. A. Brock, et al., A test for independence based on the correlation dimension, Econometric Reviews, 1996, 15: 197–235.

    Article  MATH  MathSciNet  Google Scholar 

  26. D. Hsieh, Chaos and nonlinear dynamics: Application to financial markets, Journal of Finance, 1991, 46: 1839–1877.

    Article  Google Scholar 

  27. D. Hsieh, Nonlinear dynamics in financial markets: Evidence and implications, Financial Analysts Joumal, 1995, 51(4): 55–62.

    Article  Google Scholar 

  28. M. S. Bartlett, Chance or chaos? Journal of the Royal Statistical Society, Series B, 1990, (153) (Part 3): 321–347.

  29. C. Kyrtsou and M. Terraza, Stochastic chaos or ARCH effects in stock series? A comparative study, International Review of Financial Analysis, 2002, 11(4): 407–431.

    Google Scholar 

  30. C. Kyrtsou and M. Terraza, Is it possible to study chaotic and ARCH behaviour jointly? Application of a noisy Mackey-Glass equation with heteroskedastic errors to the Paris Stock Exchange returns series, Computational Economics, 2003, 21: 257–276.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Business, Hunan Normal University, Changsha, 410081, China

    Hongquan Li

  2. Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, 100190, China

    Shouyang Wang & Wei Shang

Authors
  1. Hongquan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shouyang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wei Shang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hongquan Li.

Additional information

This research is supported by MEXT Global COE Program (Kyoto University), National Natural Science Foundation of China under Grant No.71001036 and No. 71171186, Main Direction Program of Chinese Academy of Sciences KACX1-YW-0906, and the Scientific Research Fund of Hunan Provincial Education Department under Grant No. 10A082.

This paper was recommended for publication by Editor Xiaoguang YANG.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, H., Wang, S. & Shang, W. Heterogeneity, nonlinearity and endogenous market volatility. J Syst Sci Complex 24, 1130–1142 (2011). https://doi.org/10.1007/s11424-011-9054-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-011-9054-8

Key words

Search

Navigation