Estimating Value at Risk and Expected Shortfall Using Expectiles

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309 citations0/0 files storedJournal of Financial Econometrics

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Financial Risk and Volatility Modeling Stochastic processes and financial applications Risk and Portfolio Optimization

Abstract

Expectile models are derived using asymmetric least squares. A simple formula has been presented that relates the expectile to the expectation of exceedances beyond the expectile. We use this as the basis for estimating the expected shortfall. It has been proposed that the θ quantile be estimated by the expectile for which the proportion of observations below the expectile is θ. In this way, an expectile can be used to estimate value at risk. Using expectiles has the appeal of avoiding distributional assumptions. For univariate modeling, we introduce conditional autoregressive expectiles (CARE). Empirical results for the new approach are competitive with established benchmarks methods.

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References

1993On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks 1999Coherent Measures of Risk 1998Evaluating Interval Forecasts 2004CAViaR 2000Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach 2002On the coherence of expected shortfall 2003Forecasting Volatility in Financial Markets: A Review 2005Value-at-Risk Prediction: A Comparison of Alternative Strategies

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2019Dynamic semiparametric models for expected shortfall (and Value-at-Risk)2008Assessing value at risk with CARE, the Conditional Autoregressive Expectile models 2015Risk management with expectiles 2009Conditional Quantile Estimation for Generalized Autoregressive Conditional Heteroscedasticity Models 2008Using Exponentially Weighted Quantile Regression to Estimate Value at Risk and Expected Shortfall 2017Estimation of Tail Risk Based on Extreme Expectiles

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