COMPUTING THE PORTFOLIO CONDITIONAL VALUE-AT-RISK IN THE
-STABLE CASE
Stoyan Stoyanov
Gennady Samorodnitsky
Svetlozar T. Rachev
Sergio Ortobelli
Abstract: The class of -stable distributions is an attractive probabilistic model of asset
returns distribution in the field of finance. When dealing with real issues, such as optimal
portfolio selection, it is important that we can compute the Conditional Value-at-Risk (CVaR)
accurately. The CVaR is also known as the expected tail loss (ETL) proposed in literature as a
coherent risk measure. In our paper we propose an integral expression for the calculation of
the CVaR of a stable law. We compare the current approach to some existing method and we
demonstrate how to relate the derived result to some common multivariate distributional
assumptions.
2000 AMS Mathematics Subject Classification: 60E07, 91B28, 90B50.
Key words and phrases: Stable distributions, heavy tails, coherent risk measures,
conditional value-at-risk, expected tail loss.