Lévy Copulas: Review of recent results

Peter Tankov

doi:10.1007/978-3-319-25826-3_7

Lévy Copulas: Review of recent results

Peter Tankov

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

We review and extend the now considerable literature on Lévy copulas. First, we focus on Monte Carlo methods and present a new robust algorithm for the simulation of multidimensional Lévy processes with dependence given by a Lévy copula. Next, we review statistical estimation techniques in a parametric and a non-parametric setting. Finally, we discuss the interplay between Lévy copulas and multivariate regular variation and briefly review the applications of Lévy copulas in risk management. In particular, we provide a new easy-to-use sufficient condition for multivariate regular variation of Lévy measures in terms of their Lévy copulas.

Original language	English
Title of host publication	The Fascination of Probability, Statistics and their Applications
Subtitle of host publication	In Honour of Ole E. Barndorff-Nielsen
Publisher	Springer International Publishing
Pages	127-151
Number of pages	25
ISBN (Electronic)	9783319258263
ISBN (Print)	9783319258249
DOIs	https://doi.org/10.1007/978-3-319-25826-3_7
Publication status	Published - 1 Jan 2015
Externally published	Yes

Keywords

Lévy copulas
Lévy processes
Monte Carlo simulation
Regular variation
Risk management
Statistical estimation

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10.1007/978-3-319-25826-3_7

Cite this

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title = "L{\'e}vy Copulas: Review of recent results",

abstract = "We review and extend the now considerable literature on L{\'e}vy copulas. First, we focus on Monte Carlo methods and present a new robust algorithm for the simulation of multidimensional L{\'e}vy processes with dependence given by a L{\'e}vy copula. Next, we review statistical estimation techniques in a parametric and a non-parametric setting. Finally, we discuss the interplay between L{\'e}vy copulas and multivariate regular variation and briefly review the applications of L{\'e}vy copulas in risk management. In particular, we provide a new easy-to-use sufficient condition for multivariate regular variation of L{\'e}vy measures in terms of their L{\'e}vy copulas.",

keywords = "L{\'e}vy copulas, L{\'e}vy processes, Monte Carlo simulation, Regular variation, Risk management, Statistical estimation",

author = "Peter Tankov",

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AB - We review and extend the now considerable literature on Lévy copulas. First, we focus on Monte Carlo methods and present a new robust algorithm for the simulation of multidimensional Lévy processes with dependence given by a Lévy copula. Next, we review statistical estimation techniques in a parametric and a non-parametric setting. Finally, we discuss the interplay between Lévy copulas and multivariate regular variation and briefly review the applications of Lévy copulas in risk management. In particular, we provide a new easy-to-use sufficient condition for multivariate regular variation of Lévy measures in terms of their Lévy copulas.

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KW - Lévy processes

KW - Monte Carlo simulation

KW - Regular variation

KW - Risk management

KW - Statistical estimation

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EP - 151

BT - The Fascination of Probability, Statistics and their Applications

PB - Springer International Publishing

ER -

Lévy Copulas: Review of recent results

Abstract

Keywords

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