Modelling tail risk with tempered stable distributions

an overview

Research output: Contribution to journalArticleResearchpeer-review

Abstract

In this study, we investigate the performance of different parametric models with stable and tempered stable distributions for capturing the tail behaviour of log-returns (financial asset returns). First, we define and discuss the properties of stable and tempered stable random variables. We then show how to estimate their parameters and simulate them based on their characteristic functions. Finally, as an illustration, we conduct an empirical analysis to explore the performance of different models representing the distributions of log-returns for the S&P500 and DAX indexes.

Original languageEnglish
JournalAnnals of Operations Research
DOIs
Publication statusAccepted/In press - 1 Jan 2019

Keywords

  • Lévy process
  • Stable distribution
  • Tail risk
  • Tempered stable distribution

Cite this

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title = "Modelling tail risk with tempered stable distributions: an overview",
abstract = "In this study, we investigate the performance of different parametric models with stable and tempered stable distributions for capturing the tail behaviour of log-returns (financial asset returns). First, we define and discuss the properties of stable and tempered stable random variables. We then show how to estimate their parameters and simulate them based on their characteristic functions. Finally, as an illustration, we conduct an empirical analysis to explore the performance of different models representing the distributions of log-returns for the S&P500 and DAX indexes.",
keywords = "L{\'e}vy process, Stable distribution, Tail risk, Tempered stable distribution",
author = "Hasan Fallahgoul and Gregoire Loeper",
year = "2019",
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doi = "10.1007/s10479-019-03204-3",
language = "English",
journal = "Annals of Operations Research",
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Modelling tail risk with tempered stable distributions : an overview. / Fallahgoul, Hasan; Loeper, Gregoire.

In: Annals of Operations Research, 01.01.2019.

Research output: Contribution to journalArticleResearchpeer-review

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AB - In this study, we investigate the performance of different parametric models with stable and tempered stable distributions for capturing the tail behaviour of log-returns (financial asset returns). First, we define and discuss the properties of stable and tempered stable random variables. We then show how to estimate their parameters and simulate them based on their characteristic functions. Finally, as an illustration, we conduct an empirical analysis to explore the performance of different models representing the distributions of log-returns for the S&P500 and DAX indexes.

KW - Lévy process

KW - Stable distribution

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