Given the growing need for managing financial risk, risk prediction plays an increasing role in banking and finance. In this study we compare the out-of-sample performance of existing methods and some new models for predicting value-at-risk (VaR) in a univariate context. Using more than 30 years of the daily return data on the NASDAQ Composite Index, we find that most approaches perform inadequately, although several models are acceptable under current regulatory assessment rules for model adequacy. A hybrid method, combining a heavy-tailed generalized autoregressive conditionally heteroskedastic (GARCH) filter with an extreme value theory-based approach, performs best overall, closely followed by a variant on a filtered historical simulation, and a new model based on heteroskedastic mixture distributions. Conditional autoregressive VaR (CAViaR) models perform inadequately, though an extension to a particular CAViaR model is shown to outperform the others.

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Abstract:Both unconditional mixed-normal distributions and GARCH models with fat-tailed conditional distributions have been employed for modeling financial return data. We consider a mixed-normal distribution coupled with a GARCH-type structure which allows for conditional variance in each of the components as well as dynamic feedback between the components. Special cases and relationships with previously proposed specifications are discussed and stationarity conditions are derived. An empirical application to NASDAQindex data indicates the appropriateness of the model class and illustrates that the approach can generate a plausible disaggregation of the conditional variance process, in which the components' volatility dynamics have a clearly distinct behavior that is, for example, compatible with the well-known leverage effect.JEL Classification: C22, C51, G10

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We first demonstrate the simultaneous need for both more general GARCH structures and non‐normal innovation distributions for modelling the returns on certain return series such as the highly volatile exchange rates on East Asian currencies against the US dollar. This is accomplished not only via in‐sample goodness‐of‐fit criteria, but also in terms of the precision of Value‐at‐Risk calculations made on out‐of‐sample density predictions. Second, a forecasting strategy using weighted maximum likelihood estimation is proposed. We show that it gives rise to considerably improved forecast performance over longer horizons. Copyright © 2000 John Wiley & Sons, Ltd.

We introduce a dynamic banking-macro model, which abstains from conventional meanreversion assumptions and in which-similar to Brunnermeier and Sannikov (2010)-adverse asset-price movements and their impact on risk premia and credit spreads can induce instabilities in the banking sector. To assess such phenomena empirically, we employ a multi-regime vector autoregression (MRVAR) approach rather than conventional linear vector autoregressions. We conduct bivariate empirical analyses, using country-specific financial-stress indices and industrial production, for the U.S., the UK and the four large euro-area countries. Our MRVAR-based impulse-response studies demonstrate that, compared to a linear specification, response profiles are dependent on the current state of the economy as well as the sign and size of shocks. Previous multi-regime-based studies, focusing solely on the regime-dependence of responses, conclude that, during a high-stress period, stress-increasing shocks have more dramatic consequences for economic activity than during low stress. Conducting size-dependent response analysis, we find that this holds only for small shocks and reverses when shocks become sufficiently large to induce immediate regime switches. Our findings also suggest that, in states of high financial stress, large negative shocks to financial-stress have sizeable positive effects on real activity and support the idea of "unconventional" monetary policy measures in cases of extreme financial stress.

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