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Title: Discretization of the tail density function and adjusted evaluation measures Authors:  George-Jason Siouris - University of the Aegean (Greece) [presenting]
Alexandros Karagrigoriou - University of The Aegean (Greece)
Ilia Vonta - National Technical University of Athens (Greece)
Despoina Skilogianni - UNIVERSITY OF THE AEGEAN (Greece)
Abstract: After extensive investigation on the statistical properties of financial returns, three properties have shown to be present in most, if not all, financial returns. Their existence has been the source of most problems associated with the estimation of the underlying risk of assets. These are often called the three stylized facts of financial returns and are volatility clusters, fat tails and nonlinear dependence. In order to forecast the asset volatility, a number of different models have been developed over the years. Each of them offers an answer on a specific aspect of the problem at hand. Many of these models incorporate skewed, fat-tailed distributions. The disadvantage of this approach, is that even with the simple and well-known Student distribution closed-form expected shortfall expressions are not available. This is also the case for many asymmetric heavy-tailed distributions. We propose a discretization of the tail density function which is a logical approach for resolving the above issues, since the nature of returns is discrete, as the market always operates on a specific accuracy. As a result, with the use of adjusted evaluation measures we provide improved expected percentage shortfall estimations. Illustrative examples verify the advantages of the proposed methodology.