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Journal of Systems Science and Complexity

, Volume 27, Issue 1, pp 208–224 | Cite as

A quantitative model for intraday stock price changes based on order flows

  • Meng Li
  • Xiaofeng Hui
  • Misao Endo
  • Kazuo Kishimoto
Article

Abstract

This paper proposes a double Markov model of the double continuous auction for describing intra-day price changes. The model splits intra-day price changes as the repetition of one tick price moves and assumes order arrivals are independent Poisson random processes. The dynamic process of price formation is described by a birth-death process of the double M/M/1 server queue corresponding to the best bid/ask. The initial depths of the best bid and ask are defined as different constants depending on the last price change. Thus, the price changes in the model follow a first-order Markov process. As the initial depth of the best bid/ask is originally larger than that of the opposite side when the last price is down/up, the model may explain the negative autocorrelations of the price of the best bid/ask. The estimated parameters are based on the real tick-by-tick data of the Nikkei 225 futures listed in Osaka Stock Exchanges. The authors find the model accurately predicts the returns of Osaka Stock Exchange average.

Keywords

Intra-day price changes market microstructure order flow queuing theory 

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References

  1. [1]
    Bianchi S and Pantanella A, Modeling stock prices by multifractional Brownian motion: An improved estimation of the pointwise regularity, Quantitative Finance, 2013, 13(8): 1317–1330.CrossRefGoogle Scholar
  2. [2]
    Zheng X L and Chen B M, Modeling and forecasting of stock markets under a system adaptation framework, Journal of System Science & Complexity, 2012, 25(4): 641–674.CrossRefMathSciNetGoogle Scholar
  3. [3]
    Soofi A S, Wang S Y, and Zhang Y Q, Testing for long memory in the Asian foreign exchange rates, Journal of System Science & Complexity, 2006, 19(2): 182–190.CrossRefMATHGoogle Scholar
  4. [4]
    Garman M, Market microstructure, Journal of Financial Economics, 1976, 2: 257–275.CrossRefGoogle Scholar
  5. [5]
    Madhavan A and Smidt S, An analysis of daily changes in specialist’s inventories and quotations, Journal of Finance, 1993, 48: 1959–1628.CrossRefGoogle Scholar
  6. [6]
    Hasbrouck J and Sofianos G, The traders of market makers: An empirical analysis of NYSE specialist, Journal of Finance, 48: 1565–1594.Google Scholar
  7. [7]
    Amihud Y and Mendelson H, Dealership market: Market making with inventory, Journal of Financial Economics, 1980, 8: 31–53.CrossRefGoogle Scholar
  8. [8]
    Stoll H, The supply of dealer services in securities markets, Journal of Finance, 1978, 33: 1133–1151.CrossRefGoogle Scholar
  9. [9]
    Ho T and Stoll H, Optimal dealer pricing under transactions and return uncertainty, Journal of Financial Economics, 1981, 9: 47–73.CrossRefGoogle Scholar
  10. [10]
    O’Hara M and Oldfield G, The microeconomics of market making, Journal of Financial and Quantitative Analysis, 1986, 21: 361–376.CrossRefGoogle Scholar
  11. [11]
    Hakansson N H, Optimal investment and consumption strategies under risk for a class of utility functions, Econometrica, 1970, 38: 587–607.CrossRefMATHGoogle Scholar
  12. [12]
    Mendelson H, Market Behavior in a clearing house, Econometrica, 1982, 50: 1505–1524.CrossRefMATHGoogle Scholar
  13. [13]
    Cohen K, Conroy R, and Maier S, Market Making and the Changing Structure of the Securities Industry, Rowman and Littlefield, Lanham, 1985.Google Scholar
  14. [14]
    Domowitz I and Wang J, Auctions as algorithms: Computerized trade execution and price discovery, Journal of Economic Dynamics and Control, 1994, 18: 29–60.CrossRefMATHGoogle Scholar
  15. [15]
    Luckock H, A steady-state model of the continuous double auction, Quantitative Finance, 2003, 3: 385–404.CrossRefMathSciNetGoogle Scholar
  16. [16]
    Tang L and Tian G, Reaction-diffusion-branching models of stock price fluctuations, Physica A: Statistical Mechanics and Its Applications, 1999, 264: 543–550.CrossRefMathSciNetGoogle Scholar
  17. [17]
    Maslov S, Simple model of a limit order-driven market, Physica A: Statistical Mechanics and Its Applications, 2000, 278: 571–578.CrossRefGoogle Scholar
  18. [18]
    Slanina F, Mean-field approximation for a limit order driven market model, Physical Review E, 2001, 64(5): 056136.CrossRefGoogle Scholar
  19. [19]
    Daniels M, Farmer J, Iori G, and Smith E, Quantitative model of price diffusion and market friction based on trading as a mechanistic random process, Physical Review Letters, 2003, 90(10): 108102.CrossRefGoogle Scholar
  20. [20]
    Smith E, Farmer J, Gillemot L, and Krishnamurthy S, Statistical theory of the continuous double auction, Quantitative Finance, 2003, 3: 481–514.CrossRefMathSciNetGoogle Scholar
  21. [21]
    Farmer J, Patelli P, and Zovko I, The predictive power of zero intelligence in financial markets, Technical Report, Santa Fe Institute Working Paper, 2003.Google Scholar
  22. [22]
    Li M, Endo M, Zuo S, and Kishimoto K, Order imbalances explain 90% of returns of Nikkei 225 futures, Applied Economics Letters, 2010, 17: 1241–1245.CrossRefGoogle Scholar
  23. [23]
    Endo M, Zuo S, and Kishimoto K, Modelling intra-day stock price changes in terms of a continuous double auction system, Transactions of the Japan Society for Industrial and Applied Mathematics, 2006, 16: 305–316.Google Scholar
  24. [24]
    Suzuki T, Queueing, A Library of Basal Mathematics (in Japanese), Shokabo, Tokyo, 1972.Google Scholar

Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Meng Li
    • 1
  • Xiaofeng Hui
    • 1
  • Misao Endo
    • 2
  • Kazuo Kishimoto
    • 3
  1. 1.School of ManagementHarbin Institute of TechnologyHarbinChina
  2. 2.Socio-economic Research CenterCentral Research Institute of Electric Power IndustryTokyoJapan
  3. 3.Graduate School of Systems & Information EngineeringUniversity of TsukubaIbaraki-kenJapan

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