Parameter Estimation of a Generalized Langevin Equation of Market Price

  • Min G. Lee
  • Akihiko Oba
  • Hideki Takayasu
Conference paper


This paper describes the parameter estimation of a generalized Langevin-type equation, which can be used as a model for nonlinear price dynamics in a stock market. One of the authors (H.T.) has derived a generalized Langevin equation in a discrete time frame, describing evolving price dynamics by a theoretical consideration of dealers’ behavior. With the ultimate goal of practical implementation of the model, we here attempt to estimate the random parameters that are critical for the model, by using a time series of intradaily tick-by-tick market data.

Key Words

Price dynamics Langevin equation Stochastic coefficients Parameter estimation 


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  1. [1]
    Farmer, J.D., and Sidorowich, J.J. (1987) Predicting Chaotic Time Series, Physics Review Letter, 59, pp. 845–848.MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    LeBaron, B., (1992) Forecast Improvements Using a Volatility Index, J. Applied Econometrics, 7, pp. 137–149.CrossRefGoogle Scholar
  3. [3]
    LeBaron, B., (1994) Chaos and Nonlinear Forecastability in Economics and Finance, Phil. Trans. Royal Soc. Lond. A, 348, pp. 397–404.MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. [4]
    Sato, A., and Takayasu, M., (1998) Dynamic Numerical Models of Stock Market Price: From Microscopic Determinism to Macroscopic Randomness, Physica A, 250, pp. 231–252zbMATHCrossRefGoogle Scholar
  5. [5]
    Takayasu, H., and Takayasu, M., (1999) Critical Fluctuations of Demand and Supply, Physica A, 269, pp. 24–29.ADSCrossRefGoogle Scholar
  6. [6]
    Takayasu, H., Miura, H., Hirabayashi, T., and Hamada, K.,(1992) Statistical Properties of Deterministic Threshold Elements: The Case of Market Price, Physica A, 184, pp. 127–134.ADSCrossRefGoogle Scholar
  7. [7]
    Tice, J., and Webber, N., (1997) A Nonlinear Model of the Term Structure of Interest Rates, Mathematical Finance, 7, pp. 177–209.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Japan 2002

Authors and Affiliations

  • Min G. Lee
    • 1
  • Akihiko Oba
    • 1
  • Hideki Takayasu
    • 2
  1. 1.The Nomura Securities Co., Ltd.Tokyo, Chiyoda-kuJapan
  2. 2.Sony CSL Inc.Shinagawa-ku, TokyoJapan

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