Value at Risk has become the standard measure of market risk employed by financial institutions for both internal and regulatory purposes. Despite its conceptual simplicity, its measurement is a very challenging statistical problem and none of the methodologies developed so far give satisfactory solutions.Interpreting Value at Risk as a quantile of future portfolio values conditional on current information, we propose a new approach to quantile estimation which does not require any of the extreme assumptions invoked by existing methodologies (such as normality or i.i. d. returns). The Conditional Value at Risk orCAViaR model moves the focus of attention from the distribution of returns directly to the behavior of the quantile. We postulate a variety of dynamic processes for updating the quantile and use regression quantile estimation to determine the parameters of the updating process. Tests of model adequacy utilize the criterion that each period the probability of exceeding the VaR must be independent of all the past information. We use a differential evolutionary genetic algorithm to optimize an objective function which is non-differentiable and hence cannot be optimized using traditional algorithms. Applications to simulated and real data provide empirical support to our methodology and illustrate the ability of these algorithms to adapt to new risk environments.

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Note: This Working Paper should not be reported as representing the views of the European Central Bank (ECB). Terms of use: Documents inThe views expressed are those of the authors and do not necessarily reflect those of the ECB Abstract This paper proposes methods for estimation and inference in multivariate, multi-quantile models. The theory can simultaneously accommodate models with multiple random variables, multiple con dence levels, and multiple lags of the associated quantiles. The proposed framework can be conveniently thought of as a vector autoregressive (VAR) extension to quantile models. We estimate a simple version of the model using market equity returns data to analyse spillovers in the values at risk (VaR) between a market index and nancial institutions. We construct impulse-response functions for the quantiles of a sample of 230 nancial institutions around the world and study how nancial institution-speci c and system-wide shocks are absorbed by the system. We show how the long-run risk of the largest and most leveraged nancial institutions is very sensitive to market wide shocks in situations of nancial distress, suggesting that our methodology can prove a valuable addition to the traditional toolkit of policy makers and supervisors. Non-technical summaryThe nancial crisis which started in 2007 has had a deep impact on the conceptual thinking of systemic risk among both academics and policy makers. There has been a recognition of the shortcomings of the measures that are tailored to dealing with institution-level risks. In particular, institution level Value at Risk (VaR) measures miss important externalities associated with the need to bail out systemically important banks: government and supervisory authorities may nd themselves compelled to save ex post systemically important nancial institutions, while these ignore ex ante any negative externalities associated with their behaviour. As a consequence, in the current policy debate, great emphasis has been put on how to measure the additional capital needed by nancial institutions in a situation of generalized market distress. One necessary input for the implementation of these measures is an estimate of the sensitivity of risk of nancial institutions to shocks to the whole nancial system. Since risks are intimately linked to the tails of the distribution of a random variable, this requires an econometric analysis of the interdependence between the tails of the distributions of di erent ...

"Spreads between euro area government bond yields are related to short-term interest rates, which are in turn related to market liquidity, to cyclical conditions, and to investors' incentives to take risk. In theory, lower interest rates are associated with lower degrees of risk aversion and smaller government bond spreads. Empirically, the Eurosystem's short-term interest rates are positively related to those spreads, which our econometric model finds to include significant and policy-relevant default risk and liquidity risk components." Copyright (c) CEPR, CES, MSH, 2009.

This paper presents a framework to model duration, volume and returns simultaneously, obtaining an econometric reduced form that incorporates causal and feedback effects among these variables. The methodology is applied to two groups of stocks, classified according to trade intensity. We find that: (1) all stocks exhibit trading volume clustering (which is significantly higher for frequently traded stocks); (2) times of greater activity coincide with a higher number of informed traders present in the market only for the frequently traded stocks; (3) the more frequently traded stocks converge more rapidly (in calendar time) to their longrun equilibrium, after an initial perturbation. r 2005 Elsevier B.V. All rights reserved.JEL classification: C32; G14