Nonparametric Estimation of Expected Shortfall

By S. Chen. 2007

173 citations recorded by the source corpus.

The expected shortfall is an increasingly popular risk measure in financial risk management and it possesses the desired sub-additivity property, which is lacking for the value at risk (VaR). We consider two nonparametric expected shortfall estimators for dependent financial losses. One is a sample average of excessive losses larger than a VaR. The other is a kernel smoothed version of the first estimator (Scaillet, 2004 Mathematical Finance), hoping that more accurate estimation can be achieved by smoothing. Our analysis reveals that the extra kernel smoothing does not produce more accurate estimation of the shortfall. This is different from the estimation of the VaR where smoothing has been shown to produce reduction in both the variance and the mean square error of estimation. Therefore, the simpler ES estimator based on the sample average of excessive losses is attractive for the shortfall estimation.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/5f5b7f12f77ea8b4bad7adc80d09fbe1926a41d7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

In Management Science and Operations Research

Citations in the corpus

Risk-parameter estimation in volatility models (2012, background): “The later equality can be established following the lines of proof of Lemma 2 in Chen (2008). Note also that, by (A.”
Model risk and capital reserves (2010, methodology): “16 For the nonparametric case, we apply the method of Chen (2008) , but we simplify by assuming independence over time.”
Hybrid Historical Simulation VaR and ES: Performance in Developed and Emerging Markets (2009, unknown): “Chen, S. X., Tang, C. Y. (2005), “Nonparametric inference of Value at Risk for dependent financial returns.”
Frontiers in VaR forecasting and backtesting (2016, background): “Therefore, ES is likely to gain prominence in the future; see, for example, Wu and Xiao (2002), Yamai and Yoshiba (2005), Komunjer (2007), Chen (2008), Chen et al. (2012), Lönnbark (2013), Stoyanov et al. (2013), Brandtner (in press) and Xu (in press) for some recent references on forecasting ES.”
NONPARAMETRIC ESTIMATION OF CONDITIONAL VALUE-AT-RISK AND EXPECTED SHORTFALL BASED ON EXTREME VALUE THEORY (2016, background): “Section 2 provides a 2Also, there exists a large literature on the nonparametric estimation of unconditional value-at-risk and expected shortfall (Scaillet (2004), Chen and Tang (2005), Chen (2008), Linton and Xiao (2013), Hill (2014)) that is indirectly related to our work.”
A joint quantile and expected shortfall regression framework (2017, unknown): “in Engle and Manganelli (2004). This means we run several optimization procedures using different starting values, compare the losses of the estimates of the different optimizations and select the one with the smallest loss as our final estimate.”
Nonparametric estimation of conditional VaR and expected shortfall (2008, background): “See the book by Embrechts et al. (1997) for the excellent review on this subject and the papers by McNeil (1997), Scaillet (2005) and Chen (2006).”