The Realized Laplace Transform of Volatility

Viktor Todorov*, George Tauchen

*Corresponding author for this work

Research output: Contribution to journalArticle

36 Scopus citations

Abstract

We introduce and derive the asymptotic behavior of a new measure constructed from high-frequency data which we call the realized Laplace transform of volatility. The statistic provides a nonparametric estimate for the empirical Laplace transform function of the latent stochastic volatility process over a given interval of time and is robust to the presence of jumps in the price process. With a long span of data, that is, under joint long-span and infill asymptotics, the statistic can be used to construct a nonparametric estimate of the volatility Laplace transform as well as of the integrated joint Laplace transform of volatility over different points of time. We derive feasible functional limit theorems for our statistic both under fixed-span and infill asymptotics as well as under joint long-span and infill asymptotics which allow us to quantify the precision in estimation under both sampling schemes.

Original languageEnglish (US)
Pages (from-to)1105-1127
Number of pages23
JournalEconometrica
Volume80
Issue number3
DOIs
StatePublished - May 1 2012

Keywords

  • Central limit theorem
  • High-frequency data
  • Jumps
  • Laplace transform
  • Stochastic volatility

ASJC Scopus subject areas

  • Economics and Econometrics

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