Backtesting VaR models:a two-stage procedure

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. However, they have not succeeded yet as the developed testing frameworks have not been widely accepted. A two-stage backtesting procedure is proposed in order a model that not only forecasts VaR but also predicts the loss beyond VaR to be selected. 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 (US stock, gold and dollar-pound exchange rate 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.

Forecasting value-at-risk and expected shortfall using fractionally integrated models of conditional volatility: International evidence

“…A GARCH(1,1) specification has been selected as it has been shown that a lag of order 1 on the squared residuals and the conditional variance are sufficient to model conditional volatility (Angelidis and Degiannakis, 2007;Hansen and Lunde, 2005).…”

“…However, the proposed specification allows for discontinuous or non-synchronous trading in the stocks making up an index (see Angelidis and Degiannakis, 2007;Lo and MacKinlay, 1990). 9 The normal density function has been selected to reduce the degree of parameterisation of the model, in order to focus the analysis on the distinction between the long memory and short memory specifications for the conditional variance.…”

“…In addition to evaluating an Expected Shortfall forecast, Angelidis and Degiannakis (2007) propose measuring the squared difference of the loss using ES as VaR does not give any indication about the size of the expected loss:…”

“…For example, Laurent (2003, 2004) find the skewed Student-t APARCH model to be superior to other specifications for estimating both in-sample and out-of-sample VaR. On the other hand, Angelidis and Degiannakis (2007) conclude that the Student-t and skewed Student-t overestimate the true VaR, and consequently other distributions such as the normal may be more appropriate for the standardised residuals. There is some debate over the relative merits of conditional volatility models compared to other specifications.…”

“…The normal model has been shown by Angelidis and Degiannakis (2007) to be preferable to more parameterised distributions for the standardised residuals in some cases.…”