The Realized Laplace Transform of Volatility
21 Pages Posted: 9 Oct 2010 Last revised: 21 Jul 2011
Date Written: July 19, 2011
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 presence of jumps in the price process. With a long span of data, i.e., 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 to quantify the precision in estimation under both sampling schemes.
Keywords: Laplace transform, stochastic volatility, Central Limit Theorem, activity index, jumps, high-frequency data
JEL Classification: C51, C52, G12
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