- Università La Sapienza di Roma
Wednesday, April 20, 2016
Polo Santa Marta, Via Cantarane 24, Stanza 1.59
Recently an important debate on backtesting procedures for Value-at-Risk (VaR) and Expected Shortfall (ES) has emerged starting from the Consultative document May 2012 of the Basel Committee on Banking Supervision, see for instance Embrechts et al. (2014) and Acerbi and Szekely (2014). In this debate, elicitability has appeared as a relevant property to perform the backtesting of a risk measure and to compare different forecasting procedures. A statistical functional is elicitable if it can be defined as the unique minimiser of a suitable expected loss function, see Gneiting (2011) and the references therein. The realised expected loss can then be used to compare different forecasting procedures and to rank them consistently.
For monetary risk measures, we show that elicitability leads to a subclass of the shortfall risk measures introduced by Föllmer and Schied (2002) and we fully characterise the class of convex and coherent elicitable risk measures. We confirm that the so-called expectiles are the only coherent elicitable risk measure.
We discuss the statistical and financial relevance of the elicitability property for backtesting and highlights the properties of expectiles as a valid alternative to VaR and ES.
C. Acerbi and B. Szekely. Backtesting Expected Shortfall. Risk Magazine, 2014.
Basel Committee on Banking Supervision. Consultative Document May 2012. Fundamental review of the trading book. Basel: Bank for International Settlements, 2012.
P. Embrechts, G. Puccetti, L. Rüschendorf, R. Wang and A. Beleraj. An academic response to Basel 3.5. Risks, 2:25-48, 2014.
H. Föllmer and A. Schied. Convex measures of risk and trading constraints. Financ.
Stoch., 6:429-447, 2002.
T. Gneiting. Making and evaluating point forecasts. J. Am. Stat. Assoc., 106:746-762, 2011.