Large Deviation principles of Realized Laplace Transform of Volatility

TL;DR

This paper studies the rare event probabilities of the realized Laplace transform of volatility in high-frequency data, establishing large and moderate deviation principles to understand its tail behavior.

Contribution

It introduces the first large and moderate deviation principles for the empirical realized Laplace transform of volatility, extending the understanding of its tail asymptotics.

Findings

Established large deviation principle for ERLTV

Derived moderate deviation principle for ERLTV

Provided the rate function defined on the whole real line

Abstract

Under scenario of high frequency data, consistent estimator of realized Laplace transform of volatility is proposed by \citet{TT2012a} and related central limit theorem has been well established. In this paper, we investigate the asymptotic tail behaviour of the empirical realized Laplace transform of volatility (ERLTV). We establish both large deviation principle and moderate deviation principle for the ERLTV. The good rate function for the large deviation principle is well defined in the whole real space, which indicates a limit for the normalized logarithmic tail probability of the ERLTV. Moreover, we also derive the function-level large and moderate deviation principles for ERLTV.