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

  • David S. Bates
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    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.

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    File URL: http://www.nber.org/papers/w14913.pdf
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    Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 14913.

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    Date of creation: Apr 2009
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    Handle: RePEc:nbr:nberwo:14913
    Note: AP
    Contact details of provider: Postal: National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.
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    1. Peter Carr & Liuren Wu, 2002. "The Finite Moment Log Stable Process and Option Pricing," Finance 0207012, EconWPA.
    2. Bakshi, Gurdip & Madan, Dilip, 2000. "Spanning and derivative-security valuation," Journal of Financial Economics, Elsevier, vol. 55(2), pages 205-238, February.
    3. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    4. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    5. 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.
    6. 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, 06.
    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. 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.
    9. 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.
    10. 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.
    11. 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 233-53.
    12. 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.
    13. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
    14. Lebaron, B., 1990. "Some Relations Between Volatility And Serial Correlations In Stock Market Returns," Working papers 9002, Wisconsin Madison - Social Systems.
    15. 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.
    16. 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.
    17. Dimson, Elroy, 1979. "Risk measurement when shares are subject to infrequent trading," Journal of Financial Economics, Elsevier, vol. 7(2), pages 197-226, June.
    18. Geman, Hélyette & Carr, Peter & Madan, Dilip B. & Yor, Marc, 2003. "Stochastic Volatility for Levy Processes," Economics Papers from University Paris Dauphine 123456789/1392, Paris Dauphine University.
    19. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    20. John M. Maheu & Thomas H. McCurdy, 2003. "News Arrival, Jump Dynamics and Volatility Components for Individual Stock Returns," CIRANO Working Papers 2003s-38, CIRANO.
    21. 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.
    22. 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(03), pages 455-464, September.
    23. 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.
    24. 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.
    25. 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.
    26. 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.
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