Backtesting VaR Models: An Expected Shortfall Approach

Abstract

Academics and practitioners have extensively studied Value-at-Risk (VaR) to propose a unique risk management technique that generates accurate VaR estimations for long and short trading positions and for all types of financial assets. However, they have not succeeded yet as the testing frameworks of the proposals developed, have not been widely accepted. A two-stage backtesting procedure is proposed to select a model that not only forecasts VaR but also predicts the losses beyond VaR. Numerous conditional volatility models that capture the main characteristics of asset returns (asymmetric and leptokurtic unconditional distribution of returns, power transformation and fractional integration of the conditional variance) under four distributional assumptions (normal, GED, Student-t, and skewed Student-t) have been estimated to find the best model for three financial markets, long and short trading positions, and two confidence levels. By following this procedure, the risk manager can significantly reduce the number of competing models that accurately predict both the VaR and the Expected Shortfall (ES) measures.

Value-at-Risk and Expected Shortfall When There Is Long Range Dependence

“…Although these models can achieve accurate V aR and ESF for insample one-step ahead prediction, we find that models that account for asymmetries as well as fractional integrated parametrization of the volatility process, perform better than those that reflect only symmetry or long-memory. This confirms, the findings of Angelidis and Degiannakis (2006), in suggesting that models with fractional integration parametrization of the volatility process are necessary for accurate assessment of market risk. Long-memory in volatility models hold the promise of improved long-run volatility forecast and more accurate pricing of long-term contracts.…”

Volatility Estimators in Econometric Analysis of Risk Transfer on Capital Markets

“…Twice the Garman-Klass-Yang-Zhang with POT was indicated and once the Rogers-Satchell estimator. (Lopez, 1998), QPS II means Quadratic Probability Score function with size-adjusted loss function (Lopez, 1998), QPS III means Quadratic Probability Score function with size loss function (Blanco and Ihle, 1998), RLF means Regulatory Loss Function (Sarma et al, 2003), FLF means Firm's Loss Function (Sarma et al, 2003) with opportunity cost of capital equals 0.05, LF means Loss Function (Angelidis and Degiannakis, 2006) and OLF means Overestimation Loss Function (Fałdziński, 2011). The lowest (best) values of measures are in bold.…”

Risk contagion in the north-western and southern European stock markets

“…The main reason for this is that VaR is essentially a point estimate of the tails of the empirical distribution (Angelidis & Degiannakis, 2006). In addition, regulators also use VaR to design new regulations such as the determination of bank capital standards for market risk and the reporting requirements for the risks associated with derivatives used by corporations.…”