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.

No abstract

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

Knowledge of the statistical distribution of the prices of emission allowances, and their forecastability, are crucial in constructing, among other things, purchasing and risk management strategies in the emissions-constrained markets. This paper analyzes the two emission permits markets, CO2 in Europe, and SO2 in the US, and investigates a model for dealing with the unique stylized facts of this type of data. Its effectiveness in terms of model fit and out-of-sample value-at-risk-forecasting, as compared to models commonly used in risk-forecasting contexts, is demonstrated. An Econometric Analysis of Emission Trading Allowances November 2006Abstract World power and gas markets have a natural relationship with global tradable carbon permits markets, including the U.S. Clean Air Act Amendments and the EU Emissions Trading Scheme, the latter officially launched in January 2005. Electric utilities operate their power plants based in part on the price of the power and the relative cost of coal and natural gas. As both carbon dioxide and sulphur dioxide are by-products of the coal burning process, the new factors of SO 2 and CO 2 emissions allowances come into play in a carbon constrained economy. Now that a price has been put on such allowances, the differences in carbon intensity for coal and gas could potentially change the way companies run their power plants. Moreover, knowledge of the statistical distribution of emission trading allowances, and its forecastability, becomes crucial in constructing optimal hedging and purchasing strategies in the carbon market. This paper provides an in-depth analysis of available data addressing the unconditional tail behavior and the inherent heteroskedastic dynamics in the returns on the emissions allowances.Keywords: Environmental Finance, GARCH, Greenhouse Gases, Mixture Models, Tail Estimation. * Part of the research of the authors has been carried out within the National Centre of Competence in Research "Financial Valuation and Risk Management" (NCCR FINRISK), which is a research program supported by the Swiss National Science Foundation. Corresponding author: taschini@isb.unizh.ch.† The help from Enviros Climate Change Group as well as the data base on sulfur dioxide spot prices from the Chicago Climate Exchange are gratefully acknowledged. The authors would like to thank Pauline Barrieu, Marc Chesney, George Daskalakis, Helyette Geman, Daniel Giamouridis, Rajna Gibson, Wolfgang Härdle, Gikas Hardouvelis, Raphael Markellos, Nikitas Pittis, Dimitris Psychoyios, Costas Vorlow, and Alexander Wagner for their helpful discussions and comments. We wish to also thank Sven-C. Steude for the programming assistance on the mixed normal models used in the paper.