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The Realized Laplace Transform of Volatility

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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.

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Bibliographic Info

Paper provided by Duke University, Department of Economics in its series Working Papers with number 10-72.

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Length: 48
Date of creation: 2010
Date of revision:
Handle: RePEc:duk:dukeec:10-72

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Postal: Department of Economics Duke University 213 Social Sciences Building Box 90097 Durham, NC 27708-0097
Phone: (919) 660-1800
Fax: (919) 684-8974
Web page: http://econ.duke.edu/

Related research

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

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Cited by:
  1. Todorov, Viktor & Tauchen, George & Grynkiv, Iaryna, 2014. "Volatility activity: Specification and estimation," Journal of Econometrics, Elsevier, vol. 178(P1), pages 180-193.
  2. Reiß, Markus, 2013. "Testing the characteristics of a Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2808-2828.

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