Estimation of Jump Tails

48 Pages Posted: 14 Apr 2010 Last revised: 10 Jun 2011

See all articles by Tim Bollerslev

Tim Bollerslev

Duke University - Finance; Duke University - Department of Economics; National Bureau of Economic Research (NBER)

Viktor Todorov

Northwestern University

Multiple version iconThere are 2 versions of this paper

Date Written: June 2, 2011

Abstract

We propose a new and flexible non-parametric framework for estimating the jump tails of Itô semimartingale processes. The approach is based on a relatively simple-to-implement set of estimating equations associated with the compensator for the jump measure, or its "intensity", that only utilizes the weak assumption of regular variation in the jump tails, along with in-fill asymptotic arguments for uniquely identifying the \large" jumps from the data. The estimation allows for very general dynamic dependencies in the jump tails, and does not restrict the continuous part of the process and the temporal variation in the stochastic volatility. On implementing the new estimation procedure with actual high-frequency data for the S&P 500 aggregate market portfolio, we find strong evidence for richer and more complex dynamic dependencies in the jump tails than hitherto entertained in the literature.

Keywords: Extreme events, jumps, high-frequency data, jump tails, non-parametric estimation, stochastic volatility

JEL Classification: C13, C14, G10, G12

Suggested Citation

Bollerslev, Tim and Todorov, Viktor, Estimation of Jump Tails (June 2, 2011). Economic Research Initiatives at Duke (ERID) Working Paper No. 38. Available at SSRN: https://ssrn.com/abstract=1589753 or http://dx.doi.org/10.2139/ssrn.1589753

Tim Bollerslev (Contact Author)

Duke University - Finance ( email )

Durham, NC 27708-0120
United States
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Duke University - Department of Economics

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National Bureau of Economic Research (NBER)

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Viktor Todorov

Northwestern University ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

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