Estimating the Tails of Loss Severity via Conditional Risk Measures for the Family of Symmetric Generalised Hyperbolic Family

28 Pages Posted: 13 Mar 2015 Last revised: 30 Sep 2015

See all articles by Katja Ignatieva

Katja Ignatieva

University of New South Wales - Australian School of Business

Zinoviy Landsman

University of Haifa, Department of Statistics

Date Written: September 28, 2015

Abstract

This paper addresses one of the main challenges faced by insurance companies and risk management departments, namely, how to develop standardised framework for measuring risks of underlying portfolios and in particular, how to most reliably estimate loss severity distribution from historical data. This paper investigates tail conditional expectation (TCE) and tail variance premium (TVP) risk measures for the family of symmetric generalised hyperbolic (SGH) distributions. In contrast to a widely used Value-at-Risk (VaR) measure, TCE satisfies the requirement of the "coherent" risk measure taking into account the expected loss in the tail of the distribution while TVP incorporates variability in the tail, providing the most conservative estimator of risk. We examine various distributions from the class of SGH distributions, which turn out to fit well financial data returns and allow for explicit formulas for TCE and TVP risk measures. In parallel, we obtain asymptotic behaviour for TCE and TVP risk measures for large quantile levels. Furthermore, we extend our analysis to the multivariate framework, allowing multivariate distri- butions to model combinations of correlated risks, and demonstrate how TCE can be decomposed into individual components, representing contribution of individual risks to the aggregate portfolio risk.

Keywords: Tail value-at-risk, tail conditional expectation, tail variance premium, generalised hyperbolic distributions

Suggested Citation

Ignatieva, Katja and Landsman, Zinoviy, Estimating the Tails of Loss Severity via Conditional Risk Measures for the Family of Symmetric Generalised Hyperbolic Family (September 28, 2015). UNSW Business School Research Paper No. 2015ACTL07. Available at SSRN: https://ssrn.com/abstract=2577063 or http://dx.doi.org/10.2139/ssrn.2577063

Katja Ignatieva (Contact Author)

University of New South Wales - Australian School of Business ( email )

UNSW Business School
High St
Sydney, NSW 2052
Australia

Zinoviy Landsman

University of Haifa, Department of Statistics ( email )

Haifa, 31905
Israel
+972-4-8249003 (Phone)

HOME PAGE: http://stat.haifa.ac.il/~landsman

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