Estimating expected shortfall using a quantile function model

Estimating Value at Risk and Expected Shortfall Using Expectiles

Model Risk of Expected Shortfall

In this paper we study the model risk of Expected Shortfall (ES), extending the results of Boucher et al. (2014) on model risk of Value-at-Risk (VaR). We propose a correction formula for ES based on passing three backtests. Our results show that for the DJIA index, the smallest corrections are required for the ES estimates built using GARCH models. Furthermore, the 2.5% ES requires smaller corr...

Using Exponentially Weighted Quantile Regression to Estimate Value at Risk and Expected Shortfall

We propose exponentially weighted quantile regression (EWQR) for estimating time-varying quantiles. The EWQR cost function can be used as the basis for estimating the time-varying expected shortfall associated with the EWQR quantile forecast. We express EWQR in a kernel estimation framework, and then modify it by adapting a previously proposed double kernel estimator in order to provide greater...

Expected shortfall estimation using kernel machines †

In this paper we study four kernel machines for estimating expected shortfall, which are constructed through combinations of support vector quantile regression (SVQR), restricted SVQR (RSVQR), least squares support vector machine (LS-SVM) and support vector expectile regression (SVER). These kernel machines have obvious advantages such that they achieve nonlinear model but they do not require t...

Expected Shortfall and Beyond

Abstract. Financial institutions have to allocate so-called economic capital in order to guarantee solvency to their clients and counter parties. Mathematically speaking, any methodology of allocating capital is a risk measure, i.e. a function mapping random variables to the real numbers. Nowadays value-atrisk, which is defined as a fixed level quantile of the random variable under consideratio...