Volatility specifications versus probability distributions in VaR forecasting

Abstract

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Backtesting extreme value theory models of expected shortfall

“…The parameter δ takes values between 1.04 and 1.22, and differs significantly from 2. This result suggests that more attention should be paid to modeling the dynamics of the conditional standard deviation rather than the conditional variance, as has been pointed out for a variety of assets by Garcia-Jorcano and Novales (2017).…”

“…We will consider an APARCH specification for volatility [Ding, Granger, and Engle (1993)], which is not too restrictive since it includes as special cases some of the most standard conditional volatility models. Garcia-Jorcano and Novales (2017) show that APARCH volatility fits the data for a variety of assets better than alternative models nested in APARCH. The success in capturing the heteroscedasticity exhibited by the data may be due to the increased flexibility of the APARCH model in dealing with the power on the conditional standard deviation as a free parameter.…”

A description of the COVID-19 outbreak role in financial risk forecasting

“…To estimate the conditional mean, we use an AR(1). As stated by Garcia-Jorcano and Novales (2021) , this specification is sufficient to produce serially uncorrelated innovations. We extract the standardized residuals ( ) independently and identically distributed for each estimated model.…”

A comparison of Range Value at Risk (RVaR) forecasting models

“…Our analysis considers the AR(1)‐GARCH(1,1) model. As explained in Garcia‐Jorcano and Novales (2021), returns are not serially correlated (usually), and an AR(1) model is sufficient to model and to produce serially uncorrelated innovations for all assets. We use the GARCH model to estimate conditional standard deviation because evidence shows that this model is competitive to forecast risk measures (Righi & Ceretta, 2015; Garcia‐Jorcano & Novales, 2021).…”

“…We considered the AR (Autoregressive) ‐ GARCH (Generalized Autoregressive Heteroskedasticity) model for the univariate analysis. According to the results of Garcia‐Jorcano and Novales (2021), the performance of risk forecasting models depends more on the error distribution than the conditional volatility model. Accordingly, we forecast RVaR based on different distributions for the error term while keeping the well‐established GARCH specification for conditional volatility.…”