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Application of Poisson Mixtures in the Estimation of Probability of Informed Trading

  • Emily Lin
  • Cheng-Few Lee
Reference work entry

Abstract

This research first discusses the evolution of probability for informed trading in finance literature. Motivated by asymmetric effects, e.g., return and trading volume in up and down markets, this study modifies a mixture of the Poisson distribution model by different arrival rates of informe d buys and sells to measure the probability of informed trading proposed by Easley et al. (Journal of Finance 51:1405–1436, 1996).

By applying the expectation–maximization (EM) algorithm to estimate the parameters of the model, we derive a set of equations for maximum likelihood estimation, and these equations are encoded in a SAS Macro utilizing SAS/IML for implementation of the methodology.

Keywords

Probability of informed trading (PINExpectation–maximization (EM) algorithm A mixture of Poisson distribution Asset-pricing returns Order imbalance Information asymmetry Bid–ask spreads Market microstructure Trade direction Errors in variables GARCH 

Notes

Acknowledgments

Special thanks to professors Lii-Yuh Leu, Ren-Her Wang, and Charles Chang for their helpful comments and consultation. All errors are our own.

References

  1. Bagehot, W. (1971). The only game in town. Financial Analysis Journal, 27, 12–14.CrossRefGoogle Scholar
  2. Boehmer, E., Gramming, J., & Theissen, E. (2007). Estimating the probability of informed trading-does trade misclassification matter? Journal of Financial Markets, 10, 26–47.CrossRefGoogle Scholar
  3. Bollen, N. P., Smith, T., & Whaley, R. E. (2004). Modeling the bid/ask spread: Measuring the inventory-holding premium. Journal of Financial Economics, 72, 97–141.CrossRefGoogle Scholar
  4. Bookstein, A., & Swanson, D. (1974). Probabilistic models for automatic indexing. Journal of the American Society for Information Science, 25(5), 312–318.CrossRefGoogle Scholar
  5. Brennan, M. J., & Subrahmanyam, A. (1996). Market microstructure and asset pricing: On the compensation for illiquidity in stock returns. Journal of Financial Economics, 41, 441–464.CrossRefGoogle Scholar
  6. Chang, C., & Lin, E. (2014). On the determinants of basis spread for Taiwan index futures and the role of speculators. Review of Pacific Basin Financial Markets and Policies, 17(1), 1450002-1–1450002-30.Google Scholar
  7. Church, K. W., & Gale, W. A. (1995). Poisson mixtures. Natural Language Engineering, 1(2), 163–190.CrossRefGoogle Scholar
  8. Copeland, T. E., & Galai, D. (1983). Information effects on the bid-ask spread. Journal of Finance, 38, 1457–1469.CrossRefGoogle Scholar
  9. Duarte, J., & Young, L. (2009). Why is PIN priced? Journal of Financial Economics, 91(2), 119–138.Google Scholar
  10. Easley, D., Kiefer, N., O’Hara, M., & Paperman, J. B. (1996). Liquidity, information and infrequently traded stocks. Journal of Finance, 51, 1405–1436.CrossRefGoogle Scholar
  11. Easley, D., Hvidkjaer, S., & O’Hara, M. (2002). Is information risk a determinant of asset returns? Journal of Finance, 57, 2185–2221.CrossRefGoogle Scholar
  12. Easley, D., Engle, R. F., O’Hara, M., & Wu, L. (2008). Time-varying arrival rates of informed and uninformed traders. Journal of Financial Econometrics, 6, 171–207.CrossRefGoogle Scholar
  13. Easley, D., de Prado López, M., & O’Hara, M. (2012). Flow toxicity and liquidity in a high frequency world. Review of Financial Studies, 25(5), 1457–1493.CrossRefGoogle Scholar
  14. Ellis, K., Michaely, R., & O’Hara, M. (2000). The accuracy of trade classification rules: Evidence from Nasdaq. Journal of Financial and Quantitative Analysis, 35, 529–551.CrossRefGoogle Scholar
  15. Foster, F. D., & Viswanathan, S. (1993). Variations in trading volume, return volatility, and trading costs: Evidence on recent price formation models. Journal of Finance, 48, 187–211.Google Scholar
  16. Glosten, L. R., & Harris, L. E. (1988). Estimating the components of the bid/ask spread. Journal of Financial Economics, 21, 123–142.CrossRefGoogle Scholar
  17. Hasbrouck, J. (1991). Measuring the information content of stock trades. Journal of Finance, 46, 179–207.CrossRefGoogle Scholar
  18. Johnson, N., & Kotz, S. (1969). Discrete distributions. Boston: Houghton Mifflin.Google Scholar
  19. Lee, C. F., & Chen, H. Y. (2012). Alternative errors-in-variable models and their applications in finance research. Rutgers University working paper.Google Scholar
  20. Lee, C., & Ready, M. (1991). Inferring trade direction from intraday data. Journal of Finance, 46, 733–747.CrossRefGoogle Scholar
  21. Lei, Q., & Wu, G. (2005). Time-varying informed and uninformed trading activities. Journal of Financial Markets, 8, 153–181.CrossRefGoogle Scholar
  22. Lin, E., Lee, C. F., & Wang, K. (2013). Futures mispricing, order imbalance, and short-selling constraints. International Review of Economics and Finance, 25, 408–423.CrossRefGoogle Scholar
  23. MacKinlay, A. C., & Ramaswamy, K. (1988). Index futures arbitrage and the behavior of stock index futures prices. Review of Financial Studies, 1, 137–158.CrossRefGoogle Scholar
  24. Madhavan, A., & Smidt, S. (1991). A Bayesian Model of intraday specialist pricing. Journal of Financial Economics, 30, 99–134.CrossRefGoogle Scholar
  25. McLachlan, G. J., & Krishnan, T. (2008). The EM algorithm and extensions (Wiley series in Probability and Statistics; 2nd ed.). Hoboken, NJ: Wiley.CrossRefGoogle Scholar
  26. Odders-White, E. R. (2000). On the occurrence and consequences of inaccurate trade classification. Journal of Financial Markets, 3, 259–286.CrossRefGoogle Scholar
  27. Popescu, M., & Kumar, R. (2008). An ex-ante measure of the probability of informed trading. http://ssrn.com/abstract=891717

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.St. John’s UniversityNew Taipei CityTaiwan
  2. 2.Department of Finance and EconomicsRutgers Business School, Rutgers, The State University of New JerseyPiscatawayUSA
  3. 3.Graduate Institute of FinanceNational Chiao Tung UniversityHsinchuTaiwan

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