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The Realized Laplace Transform of Volatility

Author

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  • Viktor Todorov
  • George Tauchen

Abstract

We introduce a new measure constructed from high-frequency financial data which we call the Realized Laplace Transform of volatility. The statistic provides a nonparametric estimate for the empirical Laplace transform of the latent stochastic volatility process over a given interval of time. When a long span of data is used, i.e., under joint long-span and fill-in asymptotics, it is an estimate of the volatility Laplace transform. The asymptotic behavior of the statistic depends on the small scale behavior of the driving martingale. We derive the asymptotics both in the case when the latter is known and when it needs to be inferred from the data. When the underlying process is a jump-diffusion our statistic is robust to jumps and when the process is pure-jump it is robust to presence of less active jumps. We apply our results to simulated and real financial data.

Suggested Citation

  • Viktor Todorov & George Tauchen, 2010. "The Realized Laplace Transform of Volatility," Working Papers 10-72, Duke University, Department of Economics.
  • Handle: RePEc:duk:dukeec:10-72
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    References listed on IDEAS

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    1. Mark Britten-Jones & Anthony Neuberger, 2000. "Option Prices, Implied Price Processes, and Stochastic Volatility," Journal of Finance, American Finance Association, vol. 55(2), pages 839-866, April.
    2. Itamar Drechsler & Amir Yaron, 2008. "What's Vol Got to Do With It," 2008 Meeting Papers 282, Society for Economic Dynamics.
    3. Campbell, John Y. & Hentschel, Ludger, 1992. "No news is good news *1: An asymmetric model of changing volatility in stock returns," Journal of Financial Economics, Elsevier, vol. 31(3), pages 281-318, June.
    4. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, pages 579-625.
    5. Campbell, John Y, 1996. "Understanding Risk and Return," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 298-345, April.
    6. Federico M. Bandi & Benoit Perron, 2006. "Long Memory and the Relation Between Implied and Realized Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(4), pages 636-670.
    7. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
    8. Tim Bollerslev & George Tauchen & Hao Zhou, 2009. "Expected Stock Returns and Variance Risk Premia," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4463-4492, November.
    9. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    10. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    11. Bollerslev, Tim & Gibson, Michael & Zhou, Hao, 2011. "Dynamic estimation of volatility risk premia and investor risk aversion from option-implied and realized volatilities," Journal of Econometrics, Elsevier, vol. 160(1), pages 235-245, January.
    12. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 701-720, November.
    13. Epstein, Larry G & Zin, Stanley E, 1989. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework," Econometrica, Econometric Society, vol. 57(4), pages 937-969, July.
    14. Luca Benzoni & Pierre Collin-Dufresne & Robert S. Goldstein, 2005. "Can Standard Preferences Explain the Prices of out of the Money S&P 500 Put Options," NBER Working Papers 11861, National Bureau of Economic Research, Inc.
    15. repec:oxf:wpaper:264 is not listed on IDEAS
    16. Bekaert, Geert & Engstrom, Eric & Xing, Yuhang, 2009. "Risk, uncertainty, and asset prices," Journal of Financial Economics, Elsevier, vol. 91(1), pages 59-82, January.
    17. Ravi Bansal & Amir Yaron, 2004. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," Journal of Finance, American Finance Association, vol. 59(4), pages 1481-1509, August.
    18. Comte, F. & Renault, E., 1996. "Long memory continuous time models," Journal of Econometrics, Elsevier, vol. 73(1), pages 101-149, July.
    19. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2004. "Analytical Evaluation Of Volatility Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(4), pages 1079-1110, November.
    20. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
    21. Bollerslev, Tim & Zhou, Hao, 2006. "Volatility puzzles: a simple framework for gauging return-volatility regressions," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 123-150.
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    Citations

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    Cited by:

    1. Cuchiero, Christa & Teichmann, Josef, 2015. "Fourier transform methods for pathwise covariance estimation in the presence of jumps," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 116-160.
    2. Todorov, Viktor & Tauchen, George & Grynkiv, Iaryna, 2014. "Volatility activity: Specification and estimation," Journal of Econometrics, Elsevier, vol. 178(P1), pages 180-193.
    3. repec:eee:econom:v:200:y:2017:i:1:p:36-47 is not listed on IDEAS
    4. repec:oup:biomet:v:104:y:2017:i:2:p:397-410. is not listed on IDEAS
    5. Li, Gang & Zhang, Chu, 2016. "On the relationship between conditional jump intensity and diffusive volatility," Journal of Empirical Finance, Elsevier, vol. 37(C), pages 196-213.
    6. Li, Jia & Todorov, Viktor & Tauchen, George, 2016. "Inference theory for volatility functional dependencies," Journal of Econometrics, Elsevier, vol. 193(1), pages 17-34.
    7. Reiß, Markus, 2013. "Testing the characteristics of a Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2808-2828.
    8. Jia Li & Andrew J. Patton, 2013. "Asymptotic Inference about Predictive Accuracy Using High Frequency Data," Working Papers 13-27, Duke University, Department of Economics.
    9. repec:eee:econom:v:201:y:2017:i:2:p:417-432 is not listed on IDEAS

    More about this item

    Keywords

    Laplace transform; stochastic volatility; Central Limit Theorem; activity index; jumps; high-frequency data;

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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