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The Realized Laplace Transform of Volatility


  • Viktor Todorov
  • George Tauchen


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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    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


    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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