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Methodological issues in asset pricing: Random walk or chaotic dynamics

In: Economic Uncertainty, Instabilities And Asset Bubbles Selected Essays

Author

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  • A. G. Malliaris

    (Department of Economics, Loyola University, 820 N. Michigan Avenue, Chicago, IL 60611, USA)

  • Jerome L. Stein

    (Division of Applied Mathematics, Brown University, Box F, Providence, RI 02912, USA)

Abstract

AbstractWe analyze the theoretical foundations of the efficient market hypothesis by stressing the efficient use of information and its effect upon price volatility. The "random walk" hypothesis assumes that price volatility is exogenous and unexplained. Randomness means that a knowledge of the past cannot help to predict the future. We accept the view that randomness appears because information is incomplete. The larger the subset of information available and known, the less emphasis one must place upon the generic term randomness. We construct a general and well accepted intertemporal price determination model, and show that price volatility reflects the output of a higher order dynamic system with an underlying stochastic foundation. Our analysis is used to explain the learning process and the efficient use of information in our archetype model. We estimate a general unrestricted system for financial and agricultural markets to see which specifications we can reject. What emerges is that a system very close to our archetype model is consistent with the evidence. We obtain an equation for price volatility which looks a lot like the GARCH equation. The price variability is a serially correlated variable which is affected by the Bayesian error, and the Bayesian error is a serially correlated variable which is affected by the noisiness of the system. In this manner we have explained some of the determinants of what has been called the "randomness" of price changes.

Suggested Citation

  • A. G. Malliaris & Jerome L. Stein, 2005. "Methodological issues in asset pricing: Random walk or chaotic dynamics," World Scientific Book Chapters,in: Economic Uncertainty, Instabilities And Asset Bubbles Selected Essays, chapter 8, pages 85-115 World Scientific Publishing Co. Pte. Ltd..
  • Handle: RePEc:wsi:wschap:9789812701015_0008
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    References listed on IDEAS

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    1. Baumol, William J & Benhabib, Jess, 1989. "Chaos: Significance, Mechanism, and Economic Applications," Journal of Economic Perspectives, American Economic Association, vol. 3(1), pages 77-105, Winter.
    2. Kandel, Eugene & Pearson, Neil D, 1995. "Differential Interpretation of Public Signals and Trade in Speculative Markets," Journal of Political Economy, University of Chicago Press, vol. 103(4), pages 831-872, August.
    3. Stein, Jerome L, 1992. "Price Discovery Processes," The Economic Record, The Economic Society of Australia, vol. 0(0), pages 34-45, Supplemen.
    4. Stein, Jerome L, 1992. "Cobwebs, Rational Expectations and Futures Markets," The Review of Economics and Statistics, MIT Press, vol. 74(1), pages 127-134, February.
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    Citations

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    Cited by:

    1. Paul De Grauwe & Marianna Grimaldi, 2003. "Intervention in the Foreign Exchange Market in a Model with Noise Traders," Working Papers 162003, Hong Kong Institute for Monetary Research.
    2. Catherine Kyrtsou & Michel Terraza, 2003. "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, Springer;Society for Computational Economics, vol. 21(3), pages 257-276, June.
    3. Catherine Kyrtsou & Michel Terraza, 2010. "Seasonal Mackey–Glass–GARCH process and short-term dynamics," Empirical Economics, Springer, vol. 38(2), pages 325-345, April.
    4. Leontitsis, Alexandros & Vorlow, Constantinos E., 2006. "Accounting for outliers and calendar effects in surrogate simulations of stock return sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(2), pages 522-530.
    5. Shafiqur Rahman & M. Shahid Ebrahim, 2005. "The Futures Pricing Puzzle," Computing in Economics and Finance 2005 35, Society for Computational Economics.
    6. Yankou Diasso, 2014. "Dynamique du prix international du coton : aléas, aversion au risque et chaos," Recherches économiques de Louvain, De Boeck Université, vol. 80(4), pages 53-86.
    7. Kyrtsou, Catherine & Terraza, Michel, 2002. "Stochastic chaos or ARCH effects in stock series?: A comparative study," International Review of Financial Analysis, Elsevier, vol. 11(4), pages 407-431.
    8. Kyrtsou, Catherine & Malliaris, Anastasios G., 2009. "The impact of information signals on market prices when agents have non-linear trading rules," Economic Modelling, Elsevier, vol. 26(1), pages 167-176, January.
    9. Catherine Kyrtsou & Michel Terraza, 2000. "Is It Possible To Study Jointly Chaotic And Arch Behaviour? Application Of A Noisy Mackey-Glass Equation With Heteroskedastic Errors To The Paris Stock Exchange," Computing in Economics and Finance 2000 Z226, Society for Computational Economics.
    10. Catherine Kyrtsou & Walter C. Labys & Michel Terraza, 2004. "Noisy chaotic dynamics in commodity markets," Empirical Economics, Springer, vol. 29(3), pages 489-502, September.
    11. Constantinos VORLOW & Antonios ANTONIOU & Catherine KYRTSOU, 2004. "Surrogate Data Analysis and Stochastic Chaotic Modelling: Application to Stock Exchange Returns Series," Computing in Economics and Finance 2004 27, Society for Computational Economics.
    12. Alvarez-Ramirez, Jose & Ibarra-Valdez, Carlos, 2001. "Modeling stock market dynamics based on conservation principles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 493-511.

    More about this item

    Keywords

    Asymptotic Economic Growth; Inflation; Interest Rates; Asset Pricing; Equity Markets; Foreign Currency; Monetary Policy; Crash;

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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