Modelling tail risk with tempered stable distributions: an overview
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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.
KeywordsLévy process Stable distribution Tail risk Tempered stable distribution
JEL classificationC5 G12
We are grateful to Frank Fabozzi, Young (Aaron) Kim, and Stoyan Stoyanov for helpful comments. We also thank the editor and two anonymous referees for insightful remarks. The Centre for Quantitative Finance and Investment Strategies has been supported by BNP Paribas.
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