Econometrica: May 2012, Volume 80, Issue 3

The Realized Laplace Transform of Volatility

https://doi.org/10.3982/ECTA9133
p. 1105-1127

Viktor Todorov, George Tauchen

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.

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Supplemental Material

Supplement to "The Realzed Laplace Transform of Volatility"

This appendix consists of a shorter section describing the added details regarding the empirical work in the paper along with a longer section that presents asymptotic results for the Realized Laplace Transform for the case in which volatility has a deterministic intraday component.

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Supplement to "The Realzed Laplace Transform of Volatility"

This zip file contains the replication files for the manuscript.

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