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Trading volume in models of financial derivatives

Author

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  • Sam Howison
  • David Lamper

Abstract

This paper develops a subordinated stochastic process model for an asset price, where the directing process is identified as information. Motivated by recent empirical and theoretical work, the paper makes 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 the model.

Suggested Citation

  • Sam Howison & David Lamper, 2001. "Trading volume in models of financial derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(2), pages 119-135.
    • Handle: RePEc:taf:apmtfi:v:8:y:2001:i:2:p:119-135
    DOI: 10.1080/13504860110074163
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    References listed on IDEAS

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    1. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    2. V. Plerou & P. Gopikrishnan & L. A. N. Amaral & M. Meyer & H. E. Stanley, 1999. "Scaling of the distribution of price fluctuations of individual companies," Papers cond-mat/9907161, arXiv.org.
    3. Tauchen, George E & Pitts, Mark, 1983. "The Price Variability-Volume Relationship on Speculative Markets," Econometrica, Econometric Society, vol. 51(2), pages 485-505, March.
    4. Harris, Lawrence, 1986. "Cross-Security Tests of the Mixture of Distributions Hypothesis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(1), pages 39-46, March.
    5. Epps, Thomas W & Epps, Mary Lee, 1976. "The Stochastic Dependence of Security Price Changes and Transaction Volumes: Implications for the Mixture-of-Distributions Hypothesis," Econometrica, Econometric Society, vol. 44(2), pages 305-321, March.
    6. Jones, Charles M & Kaul, Gautam & Lipson, Marc L, 1994. "Transactions, Volume, and Volatility," The Review of Financial Studies, Society for Financial Studies, vol. 7(4), pages 631-651.
    7. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Heiko Ebens, 2000. "The Distribution of Stock Return Volatility," NBER Working Papers 7933, National Bureau of Economic Research, Inc.
    8. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    9. 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.
    10. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-280, April.
    11. Karpoff, Jonathan M., 1987. "The Relation between Price Changes and Trading Volume: A Survey," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(1), pages 109-126, March.
    12. Carolyn W. Chang & Jack S. K. Chang, 1996. "Option Pricing with Stochastic Volatility: Information-Time vs. Calendar-Time," Management Science, INFORMS, vol. 42(7), pages 974-991, July.
    13. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
    14. Jain, Prem C, 1988. "Response of Hourly Stock Prices and Trading Volume to Economic News," The Journal of Business, University of Chicago Press, vol. 61(2), pages 219-231, April.
    15. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    16. Fama, Eugene F, 1991. "Efficient Capital Markets: II," Journal of Finance, American Finance Association, vol. 46(5), pages 1575-1617, December.
    17. 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 221-229, March.
    18. 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, April.
    19. French, Kenneth R. & Roll, Richard, 1986. "Stock return variances : The arrival of information and the reaction of traders," Journal of Financial Economics, Elsevier, vol. 17(1), pages 5-26, September.
    20. 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.
    21. Canina, Linda & Figlewski, Stephen, 1993. "The Informational Content of Implied Volatility," The Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 659-681.
    22. Lamoureux, Christopher G & Lastrapes, William D, 1994. "Endogenous Trading Volume and Momentum in Stock-Return Volatility," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 253-260, April.
    23. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    24. Chang, Carolyn W. & S.K. Chang, Jack & Lim, Kian-Guan, 1998. "Information-time option pricing: theory and empirical evidence," Journal of Financial Economics, Elsevier, vol. 48(2), pages 211-242, May.
    25. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    26. Bera, Anil K & Higgins, Matthew L, 1993. "ARCH Models: Properties, Estimation and Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 7(4), pages 305-366, December.
    27. Eric Renault & Nizar Touzi, 1996. "Option Hedging And Implied Volatilities In A Stochastic Volatility Model1," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 279-302, July.
    28. 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.
    29. Parameswaran Gopikrishnan & Vasiliki Plerou & Xavier Gabaix & H. Eugene Stanley, 2000. "Statistical Properties of Share Volume Traded in Financial Markets," Papers cond-mat/0008113, arXiv.org.
    30. Ball, Clifford A. & Roma, Antonio, 1994. "Stochastic Volatility Option Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(4), pages 589-607, December.
    31. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    32. Karpoff, Jonathan M, 1986. "A Theory of Trading Volume," Journal of Finance, American Finance Association, vol. 41(5), pages 1069-1087, December.
    33. Ross, Stephen A, 1989. " Information and Volatility: The No-Arbitrage Martingale Approach to Timing and Resolution Irrelevancy," Journal of Finance, American Finance Association, vol. 44(1), pages 1-17, March.
    34. Harris, Lawrence, 1987. "Transaction Data Tests of the Mixture of Distributions Hypothesis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(2), pages 127-141, June.
    35. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1992. "Stock Prices and Volume," The Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 199-242.
    36. 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.
    37. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    1. Leonenko, N.N. & Petherick, S. & Sikorskii, A., 2012. "A normal inverse Gaussian model for a risky asset with dependence," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 109-115.
    2. Emanuel Derman, 2002. "The perception of time, risk and return during periods of speculation," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 282-296.
    3. Emanuel Derman, 2002. "The Perception of Time, Risk and Return During Periods of Speculation," Papers cond-mat/0201345, arXiv.org.

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