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Option Pricing under Stochastic Volatility and Trading Volume

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  • Sadayuki Ono
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    Abstract

    This paper presents a pricing formula for European options derived from a model in which changes in the underlying price and trading volumes are jointly determined by exogenous events. This specification makes increments to the volatility depend on the current level of volatility and news and thereby accounts for the observed persistence in volatility. Moreover, it makes volatility an observable variable. The model accounts well for time varying volatility smiles and term structures, and that out-of-sample price forecasts for a sample of call options are superior to the benchmark ad hoc procedure of plugging implicit volatilities into the Black-Scholes formula.

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    File URL: http://www.york.ac.uk/media/economics/documents/discussionpapers/2007/0705.pdf
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    Bibliographic Info

    Paper provided by Department of Economics, University of York in its series Discussion Papers with number 07/05.

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    Date of creation: Mar 2007
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    Handle: RePEc:yor:yorken:07/05

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    Postal: Department of Economics and Related Studies, University of York, York, YO10 5DD, United Kingdom
    Phone: (0)1904 323776
    Fax: (0)1904 323759
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    Web page: http://www.york.ac.uk/economics/
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    Related research

    Keywords: Option valuation; trading volume; the stochastic volatility and volume (SVV) model;

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    3. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1992. "Stock Prices and Volume," Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 199-242.
    4. Campbell, John Y., 1999. "Asset prices, consumption, and the business cycle," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 19, pages 1231-1303 Elsevier.
    5. MacBeth, James D & Merville, Larry J, 1979. "An Empirical Examination of the Black-Scholes Call Option Pricing Model," Journal of Finance, American Finance Association, vol. 34(5), pages 1173-86, December.
    6. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    7. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
    8. Darrell Duffie & Jun Pan & Kenneth Singleton, 1999. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," NBER Working Papers 7105, National Bureau of Economic Research, Inc.
    9. 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.
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    16. Allan Timmerman & Massimo Guidolin, 2001. "Option prices and implied volatility dynamics under Bayesian learning," CeNDEF Workshop Papers, January 2001 P3, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    17. Epps, Thomas W, 1975. "Security Price Changes and Transaction Volumes: Theory and Evidence," American Economic Review, American Economic Association, vol. 65(4), pages 586-97, September.
    18. Wang, Jiang, 1994. "A Model of Competitive Stock Trading Volume," Journal of Political Economy, University of Chicago Press, vol. 102(1), pages 127-68, February.
    19. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    20. Shalen, Catherine T, 1993. "Volume, Volatility, and the Dispersion of Beliefs," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 405-34.
    21. Das, Sanjiv Ranjan & Sundaram, Rangarajan K., 1999. "Of Smiles and Smirks: A Term Structure Perspective," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(02), pages 211-239, June.
    22. 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(01), pages 109-126, March.
    23. Singleton, Kenneth J., 2001. "Estimation of affine asset pricing models using the empirical characteristic function," Journal of Econometrics, Elsevier, vol. 102(1), pages 111-141, May.
    24. Copeland, Thomas E, 1976. "A Model of Asset Trading under the Assumption of Sequential Information Arrival," Journal of Finance, American Finance Association, vol. 31(4), pages 1149-68, September.
    25. Xu, Xinzhong & Taylor, Stephen J., 1994. "The Term Structure of Volatility Implied by Foreign Exchange Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(01), pages 57-74, March.
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