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84
Modeling and Forecasting Realized Volatility
, 2002
"... this paper is built. First, although raw returns are clearly leptokurtic, returns standardized by realized volatilities are approximately Gaussian. Second, although the distributions of realized volatilities are clearly rightskewed, the distributions of the logarithms of realized volatilities are a ..."
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Cited by 544 (53 self)
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this paper is built. First, although raw returns are clearly leptokurtic, returns standardized by realized volatilities are approximately Gaussian. Second, although the distributions of realized volatilities are clearly rightskewed, the distributions of the logarithms of realized volatilities are approximately Gaussian. Third, the longrun dynamics of realized logarithmic volatilities are well approximated by a fractionallyintegrated longmemory process. Motivated by the three ABDL empirical regularities, we proceed to estimate and evaluate a multivariate model for the logarithmic realized volatilities: a fractionallyintegrated Gaussian vector autoregression (VAR) . Importantly, our approach explicitly permits measurement errors in the realized volatilities. Comparing the resulting volatility forecasts to those obtained from currently popular daily volatility models and more complicated highfrequency models, we find that our simple Gaussian VAR forecasts generally produce superior forecasts. Furthermore, we show that, given the theoretically motivated and empirically plausible assumption of normally distributed returns conditional on the realized volatilities, the resulting lognormalnormal mixture forecast distribution provides conditionally wellcalibrated density forecasts of returns, from which we obtain accurate estimates of conditional return quantiles. In the remainder of this paper, we proceed as follows. We begin in section 2 by formally developing the relevant quadratic variation theory within a standard frictionless arbitragefree multivariate pricing environment. In section 3 we discuss the practical construction of realized volatilities from highfrequency foreign exchange returns. Next, in section 4 we summarize the salient distributional features of r...
Resurrecting the (C)CAPM: A CrossSectional Test When Risk Premia Are TimeVarying
 Journal of Political Economy
, 2001
"... This paper explores the ability of conditional versions of the CAPM and the consumption CAPM—jointly the (C)CAPM—to explain the cross section of average stock returns. Central to our approach is the use of the log consumption–wealth ratio as a conditioning variable. We demonstrate that such conditio ..."
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Cited by 231 (10 self)
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This paper explores the ability of conditional versions of the CAPM and the consumption CAPM—jointly the (C)CAPM—to explain the cross section of average stock returns. Central to our approach is the use of the log consumption–wealth ratio as a conditioning variable. We demonstrate that such conditional models perform far better than unconditional specifications and about as well as the FamaFrench threefactor model on portfolios sorted by size and booktomarket characteristics. The conditional consumption CAPM can account for the difference in returns between lowbooktomarket and highbooktomarket portfolios and exhibits little evidence of residual size or booktomarket effects. We are grateful to Eugene Fama and Kenneth French for graciously providing the
How accurate are valueatrisk models at commercial banks
 Journal of Finance
, 2002
"... In recent years, the trading accounts at large commercial banks have grown substantially and become progressively more diverse and complex. We provide descriptive statistics on the trading revenues from such activities and on the associated ValueatRisk forecasts internally estimated by banks. For ..."
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Cited by 82 (1 self)
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In recent years, the trading accounts at large commercial banks have grown substantially and become progressively more diverse and complex. We provide descriptive statistics on the trading revenues from such activities and on the associated ValueatRisk forecasts internally estimated by banks. For a sample of large bank holding companies, we evaluate the performance of banks ’ trading risk models by examining the statistical accuracy of the VaR forecasts. Although a substantial literature has examined the statistical and economic meaning of ValueatRisk models, this article is the first to provide a detailed analysis of the performance of models actually in use.
A General Approach to Integrated Risk Management with Skewed, Fattailed Risks
, 2005
"... Integrated risk management in a financial institution requires an approach for aggregating risk types (market, credit, and operational) whose distributional shapes vary considerably. In this paper, we construct the joint risk distribution for a typical large, internationally active bank using the me ..."
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Cited by 67 (3 self)
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Integrated risk management in a financial institution requires an approach for aggregating risk types (market, credit, and operational) whose distributional shapes vary considerably. In this paper, we construct the joint risk distribution for a typical large, internationally active bank using the method of copulas. This technique allows us to incorporate realistic marginal distributions, both conditional and unconditional, that capture some of the essential empirical features of these risks such as skewness and fattails while allowing for a rich dependence structure. We explore the impact of business mix and interrisk correlations on total risk, whether measured by valueatrisk or expected shortfall. We find that given a risk type, total risk is more sensitive to differences in business mix or risk weights than to differences in interrisk correlations. There is a complex relationship between volatility and fattails in determining the total risk: depending on the setting, they either offset or reinforce each other. The choice of copula (normal versus Studentt), which determines the level of tail dependence, has a more modest effect on risk. We then compare the copulabased method with several conventional approaches to computing risk.
Analytic evaluation of volatility forecasts
 International Economic Review
, 2004
"... The development of estimation and forecasting procedures using empirically realistic continuoustime stochastic volatility models is severely hampered by the lack of closedform expressions for the transition densities of the observed returns. In response to this, Andersen, Bollerslev, Diebold and L ..."
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Cited by 59 (10 self)
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The development of estimation and forecasting procedures using empirically realistic continuoustime stochastic volatility models is severely hampered by the lack of closedform expressions for the transition densities of the observed returns. In response to this, Andersen, Bollerslev, Diebold and Labys (2002) have recently advocated modeling and forecasting the (latent) integrated volatility of primary import from a pricing perspective based on simple reduced form time series models for the observable realized volatilities, constructed from the summation of highfrequency squared returns. Building on the eigenfunction stochastic volatility class of models introduced by Meddahi (2001), we present analytical expressions for the loss in forecast eÆciency associated with this easytoimplement procedure as a function of the sampling frequency of the returns underlying the realized volatility measures. On numerically quantifying this eÆciency loss for such popular continuoustime models as GARCH, multifactor aÆne, and lognormal diusions, we nd that the realized volatility reduced form procedures perform remarkably well in comparison to the optimal (nonfeasible) forecasts conditional on the full sample path realization of the latent instantaneous volatility process.
Predictive density evaluation
, 2005
"... This chapter discusses estimation, specification testing, and model selection of predictive density models. In particular, predictive density estimation is briefly discussed, and a variety of different specification and model evaluation tests due to various ..."
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Cited by 46 (6 self)
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This chapter discusses estimation, specification testing, and model selection of predictive density models. In particular, predictive density estimation is briefly discussed, and a variety of different specification and model evaluation tests due to various
2004a, Term Structure of Risk Under Alternative Econometric Specifications
 Journal of Econometrics
"... This paper characterizes the term structure of risk measures such as Value at Risk (VaR) and expected shortfall under different econometric approaches including multivariate regime switching, GARCHinmean models with studentt errors, twocomponent GARCH models and a nonparametric bootstrap. We sh ..."
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Cited by 40 (5 self)
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This paper characterizes the term structure of risk measures such as Value at Risk (VaR) and expected shortfall under different econometric approaches including multivariate regime switching, GARCHinmean models with studentt errors, twocomponent GARCH models and a nonparametric bootstrap. We show how to derive the risk measures for each of these models and document large variations in term structures across econometric specifications. An outofsample forecasting experiment applied to stock, bond and cash portfolios suggests that the best model is asset and horizon specific but that the bootstrap and regime switching model are best overall for VaR levels of 5 % and 1%, respectively. Key words: term structure of risk, nonlinear econometric models, simulation methods. 1.
ValueAtRisk For Long And Short Trading Positions
, 2001
"... In this paper we model ValueatRisk (VaR) for daily stock index returns using a collection of parametric models of the ARCH family based on the skewed Student distribution. We show that models that rely on a symmetric density distribution for the error term underperform with respect to skewed de ..."
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Cited by 37 (1 self)
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In this paper we model ValueatRisk (VaR) for daily stock index returns using a collection of parametric models of the ARCH family based on the skewed Student distribution. We show that models that rely on a symmetric density distribution for the error term underperform with respect to skewed density models when the left and right tails of the distribution of returns must be modelled. Thus, VaR for traders having both long and short positions is not adequately modelled using usual Normal or Student distributions. We suggest using an APARCH model based on the skewed Student distribution to fully take into account the fat left and right tails of the returns distribution. This allows for an adequate modelling of large returns defined on long and short trading positions. The performances of all models are assessed on daily data for the CAC40, DAX, NASDAQ, NIKKEI and SMI stock indexes. We also compute the expected shortfall and the average multiple of tail event to risk measure for the new model. Keywords: ValueatRisk, Expected shortfall, Skewed Student distribution, APARCH, short trading JEL classification: C52, C53, G15 1 Department of Quantitative Economics, Maastricht University and Center for Operations Research and Econometrics, UCL; email: giot@core.ucl.ac.be or p.giot@ke.unimaas.nl 2 Departement des Sciences Economiques, Universite de Liege. This research was done when S. Laurent was visiting the Department of Quantitative Economics at Maastricht University. email: S.Laurent@ulg.ac.be 3 Corresponding author While remaining responsible for any errors in this paper, the authors would like to thank Luc Bauwens, Jon Danielsson, Philippe Lambert and JeanPierre Urbain for useful remarks and suggestions. 1
Modelling and Forecasting Stock Returns: Exploiting the Futures Market, Regime Shifts and International Spillovers
, 2001
"... A large empirical literature has reported that the futures market contains valuable information for explaining stock returns and that stock returns display significant crosscorrelations internationally. A parallel literature has recorded evidence that the distribution of stock returns is close to a ..."
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Cited by 28 (3 self)
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A large empirical literature has reported that the futures market contains valuable information for explaining stock returns and that stock returns display significant crosscorrelations internationally. A parallel literature has recorded evidence that the distribution of stock returns is close to a mixture of normal distributions and that Markov switching models may therefore provide an adequate characterization of stock returns data. This paper ties together these strands of research in that we propose a vector equilibrium correction model of stock returns that exploits the information in the futures market, while also allowing for regimeswitching behavior and international spillovers across stock market indices. Using data for three major stock market indices since 1988, we ¯nd that our model significantly outperforms a number of alternative models in sample on the basis of standard statistical criteria. In an outofsample forecasting exercise, the model produces some of the highest R² hitherto recorded in the literature and beats all of the competing models considered on the basis of density forecast accuracy.