IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/14913.html
   My bibliography  Save this paper

U.S. Stock Market Crash Risk, 1926-2006

Author

Listed:
  • David S. Bates

Abstract

This paper applies the Bates (RFS, 2006) methodology to the problem of estimating and filtering time- changed Lévy processes, using daily data on U.S. stock market excess returns over 1926-2006. In contrast to density-based filtration approaches, the methodology recursively updates the associated conditional characteristic functions of the latent variables. The paper examines how well time-changed Lévy specifications capture stochastic volatility, the "leverage" effect, and the substantial outliers occasionally observed in stock market returns. The paper also finds that the autocorrelation of stock market excess returns varies substantially over time, necessitating an additional latent variable when analyzing historical data on stock market returns. The paper explores option pricing implications, and compares the results with observed prices of options on S&P 500 futures.

Suggested Citation

  • David S. Bates, 2009. "U.S. Stock Market Crash Risk, 1926-2006," NBER Working Papers 14913, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:14913
    Note: AP
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w14913.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-778, April.
    2. Schwert, G William, 1990. "Indexes of U.S. Stock Prices from 1802 to 1987," The Journal of Business, University of Chicago Press, vol. 63(3), pages 399-426, July.
    3. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-777, April.
    4. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2002. "An Empirical Investigation of Continuous-Time Equity Return Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1239-1284, June.
    5. Torben G. Andersen & Tim Bollerslev & Peter Christoffersen & Francis X. Diebold, 2007. "Practical Volatility and Correlation Modeling for Financial Market Risk Management," NBER Chapters, in: The Risks of Financial Institutions, pages 513-548, National Bureau of Economic Research, Inc.
    6. Mark Broadie & Mikhail Chernov & Michael Johannes, 2009. "Understanding Index Option Returns," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4493-4529, November.
    7. Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July.
    8. LeBaron, Blake, 1992. "Some Relations between Volatility and Serial Correlations in Stock Market Returns," The Journal of Business, University of Chicago Press, vol. 65(2), pages 199-219, April.
    9. 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.
    10. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    11. Jokivuolle, Esa, 1995. "Measuring True Stock Index Value in the Presence of Infrequent Trading," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(3), pages 455-464, September.
    12. Hentschel, Ludger, 1995. "All in the family Nesting symmetric and asymmetric GARCH models," Journal of Financial Economics, Elsevier, vol. 39(1), pages 71-104, September.
    13. David S. Bates, 2006. "Maximum Likelihood Estimation of Latent Affine Processes," Review of Financial Studies, Society for Financial Studies, vol. 19(3), pages 909-965.
    14. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
    15. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    16. John M. Maheu & Thomas H. McCurdy, 2004. "News Arrival, Jump Dynamics, and Volatility Components for Individual Stock Returns," Journal of Finance, American Finance Association, vol. 59(2), pages 755-793, April.
    17. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    18. Bakshi, Gurdip & Madan, Dilip, 2000. "Spanning and derivative-security valuation," Journal of Financial Economics, Elsevier, vol. 55(2), pages 205-238, February.
    19. Dimson, Elroy, 1979. "Risk measurement when shares are subject to infrequent trading," Journal of Financial Economics, Elsevier, vol. 7(2), pages 197-226, June.
    20. 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.
    21. Barclay, Michael J & Litzenberger, Robert H & Warner, Jerold B, 1990. "Private Information, Trading Volume, and Stock-Return Variances," Review of Financial Studies, Society for Financial Studies, vol. 3(2), pages 233-253.
    22. 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..
    23. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    24. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    25. repec:dau:papers:123456789/1392 is not listed on IDEAS
    26. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    27. 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.
    28. Helyette Geman & P. Carr & D. Madan & M. Yor, 2003. "Stochastic Volatility for Levy Processes," Post-Print halshs-00144385, HAL.
    29. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yang Lu & Michael Siemer, 2013. "Learning, Rare Disasters, and Asset Prices," Finance and Economics Discussion Series 2013-85, Board of Governors of the Federal Reserve System (U.S.).

    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. Bates, David S., 2012. "U.S. stock market crash risk, 1926–2010," Journal of Financial Economics, Elsevier, vol. 105(2), pages 229-259.
    2. Peter Christoffersen & Kris Jacobs & Chayawat Ornthanalai, 2009. "Exploring Time-Varying Jump Intensities: Evidence from S&P500 Returns and Options," CIRANO Working Papers 2009s-34, CIRANO.
    3. Torben G. Andersen & Tim Bollerslev & Per Frederiksen & Morten Ørregaard Nielsen, 2010. "Continuous-time models, realized volatilities, and testable distributional implications for daily stock returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(2), pages 233-261.
    4. Christensen, Kim & Oomen, Roel C.A. & Podolskij, Mark, 2014. "Fact or friction: Jumps at ultra high frequency," Journal of Financial Economics, Elsevier, vol. 114(3), pages 576-599.
    5. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Center for Research in Economics and Statistics.
    6. Calvet, Laurent E. & Fisher, Adlai J., 2008. "Multifrequency jump-diffusions: An equilibrium approach," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 207-226, January.
    7. Christoffersen, Peter & Jacobs, Kris & Ornthanalai, Chayawat & Wang, Yintian, 2008. "Option valuation with long-run and short-run volatility components," Journal of Financial Economics, Elsevier, vol. 90(3), pages 272-297, December.
    8. Liu, Yi & Liu, Huifang & Zhang, Lei, 2019. "Modeling and forecasting return jumps using realized variation measures," Economic Modelling, Elsevier, vol. 76(C), pages 63-80.
    9. René Garcia & Eric Ghysels & Eric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.
    10. Li, Minqiang, 2008. "Price Deviations of S&P 500 Index Options from the Black-Scholes Formula Follow a Simple Pattern," MPRA Paper 11530, University Library of Munich, Germany.
    11. Jingzhi Huang & Liuren Wu, 2004. "Specification Analysis of Option Pricing Models Based on Time- Changed Levy Processes," Finance 0401002, University Library of Munich, Germany.
    12. Ornthanalai, Chayawat, 2014. "Lévy jump risk: Evidence from options and returns," Journal of Financial Economics, Elsevier, vol. 112(1), pages 69-90.
    13. Christoffersen, Peter & Jacobs, Kris & Ornthanalai, Chayawat, 2012. "Dynamic jump intensities and risk premiums: Evidence from S&P500 returns and options," Journal of Financial Economics, Elsevier, vol. 106(3), pages 447-472.
    14. Anatoliy Swishchuk, 2013. "Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8660, October.
    15. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.
    16. Sanjay K. Nawalkha & Xiaoyang Zhuo, 2020. "A Theory of Equivalent Expectation Measures for Expected Prices of Contingent Claims," Papers 2006.15312, arXiv.org, revised Sep 2020.
    17. Jin Zhang & Yi Xiang, 2008. "The implied volatility smirk," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 263-284.
    18. Li, Junye & Favero, Carlo & Ortu, Fulvio, 2012. "A spectral estimation of tempered stable stochastic volatility models and option pricing," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3645-3658.
    19. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    20. Kaeck, Andreas, 2013. "Asymmetry in the jump-size distribution of the S&P 500: Evidence from equity and option markets," Journal of Economic Dynamics and Control, Elsevier, vol. 37(9), pages 1872-1888.

    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • G1 - Financial Economics - - General Financial Markets
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    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:nbr:nberwo:14913. See general information about how to correct material in RePEc.

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

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.