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Trading Volume in Models of Financial Derivatives

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Author Info
Sam Howison
David lamper
Abstract

This paper develops a subordinated stochastic process model for the asset price, where the directing process is identified as information. Motivated by recent empirical and theoretical work, we make use of the under-used market statistic of transaction count as a suitable proxy for the information flow. An option pricing formula is derived, and comparisons with stochastic volatility models are drawn. Both the asset price and the number of trades are used in parameter estimation. The underlying process is found to be fast mean reverting, and this is exploited to perform an asymptotic expansion. The implied volatility skew is then used to calibrate this model.

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Paper provided by Oxford Financial Research Centre in its series OFRC Working Papers Series with number 2000mf03.

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Date of creation: 2000
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Handle: RePEc:sbs:wpsefe:2000mf03

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January. [Downloadable!] (restricted)
  2. Lamoureux, Christopher G & Lastrapes, William D, 1990. " Heteroskedasticity in Stock Return Data: Volume versus GARCH Effects," Journal of Finance, American Finance Association, vol. 45(1), pages 221-29, March. [Downloadable!] (restricted)
  3. Jain, Prem C, 1988. "Response of Hourly Stock Prices and Trading Volume to Economic News," Journal of Business, University of Chicago Press, vol. 61(2), pages 219-31, April. [Downloadable!] (restricted)
  4. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," Journal of Business, University of Chicago Press, vol. 36, pages 394. [Downloadable!]
  5. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Heiko Ebens, 2000. "The Distribution of Stock Return Volatility," Center for Financial Institutions Working Papers 00-27, Wharton School Center for Financial Institutions, University of Pennsylvania. [Downloadable!]
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  6. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March. [Downloadable!] (restricted)
  7. Bessembinder, Hendrik & Chan, Kalok & Seguin, Paul J., 1996. "An empirical examination of information, differences of opinion, and trading activity," Journal of Financial Economics, Elsevier, vol. 40(1), pages 105-134, January. [Downloadable!] (restricted)
  8. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March. [Downloadable!] (restricted)
  9. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59. [Downloadable!] (restricted)
  10. Jones, Charles M. & Kaul, Gautam & Lipson, Marc L., 1994. "Information, trading, and volatility," Journal of Financial Economics, Elsevier, vol. 36(1), pages 127-154, August. [Downloadable!] (restricted)
  11. Parameswaran Gopikrishnan & Vasiliki Plerou & Xavier Gabaix & H. Eugene Stanley, 2000. "Statistical Properties of Share Volume Traded in Financial Markets," Quantitative Finance Papers cond-mat/0008113, arXiv.org. [Downloadable!]
  12. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," Journal of Business, University of Chicago Press, vol. 47(2), pages 244-80, April. [Downloadable!] (restricted)
  13. Canina, Linda & Figlewski, Stephen, 1993. "The Informational Content of Implied Volatility," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 6(3), pages 659-81. [Downloadable!] (restricted)
  14. Ball, Clifford A. & Roma, Antonio, 1994. "Stochastic Volatility Option Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(04), pages 589-607, December. [Downloadable!]
  15. Tarun Chordia & Bhaskaran Swaminathan, 2000. "Trading Volume and Cross-Autocorrelations in Stock Returns," Journal of Finance, American Finance Association, vol. 55(2), pages 913-935, 04. [Downloadable!] (restricted)
  16. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-35, November. [Downloadable!] (restricted)
  17. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1992. "Stock Prices and Volume," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 5(2), pages 199-242. [Downloadable!] (restricted)
  18. Lux, Thomas, 1999. "Multi-Fractal Processes as Models for Financial Returns: A First Assessment," Discussion Paper Serie B 456, University of Bonn, Germany.
  19. Andersen, Torben G, 1996. " Return Volatility and Trading Volume: An Information Flow Interpretation of Stochastic Volatility," Journal of Finance, American Finance Association, vol. 51(1), pages 169-204, March. [Downloadable!] (restricted)
  20. Karpoff, Jonathan M, 1986. " A Theory of Trading Volume," Journal of Finance, American Finance Association, vol. 41(5), pages 1069-87, December. [Downloadable!] (restricted)
  21. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  22. Harris, Lawrence, 1986. "Cross-Security Tests of the Mixture of Distributions Hypothesis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(01), pages 39-46, March. [Downloadable!]
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Sam Howison & David lamper, 2001. "Trading Volume in Models of Financial Derivatives," OFRC Working Papers Series 2001mf03, Oxford Financial Research Centre. [Downloadable!]
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