IDEAS home Printed from https://ideas.repec.org/p/yor/yorken/07-05.html
   My bibliography  Save this paper

Option Pricing under Stochastic Volatility and Trading Volume

Author

Listed:
  • Sadayuki Ono

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.

Suggested Citation

  • Sadayuki Ono, 2007. "Option Pricing under Stochastic Volatility and Trading Volume," Discussion Papers 07/05, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:07/05
    as

    Download full text from publisher

    File URL: https://www.york.ac.uk/media/economics/documents/discussionpapers/2007/0705.pdf
    File Function: Main text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Shalen, Catherine T, 1993. "Volume, Volatility, and the Dispersion of Beliefs," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 405-434.
    2. Guidolin, Massimo & Timmermann, Allan, 2003. "Option prices under Bayesian learning: implied volatility dynamics and predictive densities," Journal of Economic Dynamics and Control, Elsevier, vol. 27(5), pages 717-769, March.
    3. 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.
    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    5. Christoffersen, Peter & Jacobs, Kris, 2004. "The importance of the loss function in option valuation," Journal of Financial Economics, Elsevier, vol. 72(2), pages 291-318, May.
    6. John Y. Campbell & Sanford J. Grossman & Jiang Wang, 1993. "Trading Volume and Serial Correlation in Stock Returns," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(4), pages 905-939.
    7. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    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 221-229, March.
    10. Lee, Bong-Soo & Rui, Oliver M., 2002. "The dynamic relationship between stock returns and trading volume: Domestic and cross-country evidence," Journal of Banking & Finance, Elsevier, vol. 26(1), pages 51-78, January.
    11. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    12. 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.
    13. Epps, Thomas W, 1975. "Security Price Changes and Transaction Volumes: Theory and Evidence," American Economic Review, American Economic Association, vol. 65(4), pages 586-597, September.
    14. Sheikh, Aamir M, 1993. "The Behavior of Volatility Expectations and Their Effects on Expected Returns," The Journal of Business, University of Chicago Press, vol. 66(1), pages 93-116, January.
    15. 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 1149-1168, September.
    16. Tauchen, George E & Pitts, Mark, 1983. "The Price Variability-Volume Relationship on Speculative Markets," Econometrica, Econometric Society, vol. 51(2), pages 485-505, March.
    17. 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.
    18. T W Epps, 2000. "Pricing Derivative Securities," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4415, January.
    19. 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.
    20. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    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(2), pages 211-239, June.
    22. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    23. Louis O. Scott, 1997. "Pricing Stock Options in a Jump‐Diffusion Model with Stochastic Volatility and Interest Rates: Applications of Fourier Inversion Methods," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 413-426, October.
    24. 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(1), pages 57-74, March.
    25. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    26. 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.
    27. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
    28. 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 1173-1186, December.
    29. Wang, Jiang, 1994. "A Model of Competitive Stock Trading Volume," Journal of Political Economy, University of Chicago Press, vol. 102(1), pages 127-168, February.
    30. 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.
    31. 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.
    32. 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.
    33. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    2. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    3. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    4. Ngene, Geoffrey M. & Mungai, Ann Nduati, 2022. "Stock returns, trading volume, and volatility: The case of African stock markets," International Review of Financial Analysis, Elsevier, vol. 82(C).
    5. Yamani, Ehab, 2023. "Return–volume nexus in financial markets: A survey of research," Research in International Business and Finance, Elsevier, vol. 65(C).
    6. Sarika Mahajan & Balwinder Singh, 2008. "An Empirical Analysis of Stock Price-Volume Relationship in Indian Stock Market," Vision, , vol. 12(3), pages 1-13, July.
    7. Chuang, Wen-I & Liu, Hsiang-Hsi & Susmel, Rauli, 2012. "The bivariate GARCH approach to investigating the relation between stock returns, trading volume, and return volatility," Global Finance Journal, Elsevier, vol. 23(1), pages 1-15.
    8. Go, You-How & Lau, Wee-Yeap, 2020. "The impact of global financial crisis on informational efficiency: Evidence from price-volume relation in crude palm oil futures market," Journal of Commodity Markets, Elsevier, vol. 17(C).
    9. Chuang, Wen-I & Huang, Teng-Ching & Lin, Bing-Huei, 2013. "Predicting volatility using the Markov-switching multifractal model: Evidence from S&P 100 index and equity options," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 168-187.
    10. René Garcia & Eric Ghysels & Eric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.
    11. Chuang, Chia-Chang & Kuan, Chung-Ming & Lin, Hsin-Yi, 2009. "Causality in quantiles and dynamic stock return-volume relations," Journal of Banking & Finance, Elsevier, vol. 33(7), pages 1351-1360, July.
    12. Henryk Gurgul & Roland Mestel & Tomasz Wojtowicz, 2007. "Distribution of volume on the American stock market," Managerial Economics, AGH University of Science and Technology, Faculty of Management, vol. 1, pages 143-163.
    13. Kao, Yu-Sheng & Chuang, Hwei-Lin & Ku, Yu-Cheng, 2020. "The empirical linkages among market returns, return volatility, and trading volume: Evidence from the S&P 500 VIX Futures," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    14. Koubaa, Yosra & Slim, Skander, 2019. "The relationship between trading activity and stock market volatility: Does the volume threshold matter?," Economic Modelling, Elsevier, vol. 82(C), pages 168-184.
    15. Anirut Pisedtasalasai & Abeyratna Gunasekarage, 2007. "Causal and Dynamic Relationships among Stock Returns, Return Volatility and Trading Volume: Evidence from Emerging markets in South-East Asia," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(4), pages 277-297, December.
    16. Do, Hung Xuan & Brooks, Robert & Treepongkaruna, Sirimon & Wu, Eliza, 2014. "How does trading volume affect financial return distributions?," International Review of Financial Analysis, Elsevier, vol. 35(C), pages 190-206.
    17. Loredana Ureche-Rangau & Quiterie de Rorthays, 2009. "More on the volatility-trading volume relationship in emerging markets: The Chinese stock market," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(7), pages 779-799.
    18. Kausik Chaudhuri & Alok Kumar, 2015. "A Markov-Switching Model for Indian Stock Price and Volume," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 14(3), pages 239-257, December.
    19. Robert Elliott & Tak Siu, 2015. "Asset Pricing Using Trading Volumes in a Hidden Regime-Switching Environment," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 22(2), pages 133-149, May.
    20. David McMillan & Alan Speight, 2002. "Return-volume dynamics in UK futures," Applied Financial Economics, Taylor & Francis Journals, vol. 12(10), pages 707-713.

    More about this item

    Keywords

    Option valuation; trading volume; the stochastic volatility and volume (SVV) model;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:yor:yorken:07/05. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Paul Hodgson (email available below). General contact details of provider: https://edirc.repec.org/data/deyoruk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.