Working Papers
By Year:
Paper #  Author  Title  

11037 
Torben G. Andersen Tim Bollerslev Peter F. Christoffersen Francis X. Diebold 
“Financial Risk Measurement for Financial Risk Management”  
Current practice largely follows restrictive approaches to market risk measurement, such as historical simulation or RiskMetrics. In contrast, we propose flexible methods that exploit recent developments in financial econometrics and are likely to produce more accurate risk assessments, treating both portfoliolevel and assetlevel analysis. Assetlevel analysis is particularly challenging
because the demands of realworld risk management in financial institutions—in particular, realtime risk tracking in very highdimensional situations—impose strict limits on model complexity. Hence we stress powerful yet parsimonious models that are easily estimated. In addition, we emphasize the need for deeper understanding of the links between market risk and macroeconomic
fundamentals, focusing primarily on links among equity return volatilities, real growth, and real growth volatilities. Throughout, we strive not only to deepen our scientic understanding of market risk, but also crossfertilize the academic and practitioner communities, promoting improved market risk measurement technologies that draw on the best of both. Download Paper


06016 
Peter F. Christoffersen Francis X. Diebold Roberto Mariano Anthony S. Tay Yiu Kuen Tse 
"DirectionofChange Forecasts Based on Conditional Variance, Skewness and Kurtosis Dynamics: International Evidence"  
Recent theoretical work has revealed a direct connection between asset return volatility forecastability and asset return sign forecastability. This suggests that the pervasive volatility forecastability in equity returns could, via induced sign forecastability, be used to produce directionof change forecasts useful for market timing. We attempt to do so in an international sample of developed equity markets, with some success, as assessed by formal probability forecast scoring rules such as the Brier score. An important ingredient is our conditioning not only on conditional mean and variance information, but also conditional skewness and kurtosis information, when forming directionofchange forecasts. Download Paper


05011 
Torben G. Andersen Tim Bollerslev Peter F. Christoffersen Francis X. Diebold 
"Volatility Forecasting"  
Volatility has been one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. This chapter provides a selective survey of the most important theoretical developments and empirical insights to emerge from this burgeoning literature, with a distinct focus on forecasting applications. Volatility is inherently latent, and Section 1 begins with a brief intuitive account of various key volatility concepts. Section 2 then discusses a series of different economic situations in which volatility plays a crucial role, ranging from the use of volatility forecasts in portfolio allocation to density forecasting in risk management. Sections 3, 4 and 5 present a variety of alternative procedures for univariate volatility modeling and forecasting based on the GARCH, stochastic volatility and realized volatility paradigms, respectively. Section 6 extends the discussion to the multivariate problem of forecasting conditional covariances and correlations, and Section 7 discusses volatility forecast evaluation methods in both univariate and multivariate cases. Section 8 concludes briefly. Download Paper


05007 
Torben G. Andersen Tim Bollerslev Peter F. Christoffersen Francis X. Diebold 
"Practical Volatility and Correlation Modeling for Financial Market Risk Management"  
What do academics have to offer market risk management practitioners in financial institutions? Current industry practice largely follows one of two extremely restrictive approaches: historical simulation or RiskMetrics. In contrast, we favor flexible methods based on recent developments in financial econometrics, which are likely to produce more accurate assessments of market risk. Clearly, the demands of realworld risk management in financial institutions  in particular, realtime risk tracking in very highdimensional situations  impose strict limits on model complexity. Hence we stress parsimonious models that are easily estimated, and we discuss a variety of practical approaches for highdimensional covariance matrix modeling, along with what we see as some of the pitfalls and problems in current practice. In so doing we hope to encourage further dialog between the academic and practitioner communities, hopefully stimulating the development of improved market risk management technologies that draw on the best of both worlds. Download Paper


04009 
Peter F. Christoffersen Francis X. Diebold 
"Financial Asset Returns, DirectionofChange Forecasting, and Volatility Dynamics"  
We consider three sets of phenomena that feature prominently  and separately  in the financial economics literature: conditional mean dependence (or lack thereof) in asset returns, dependence (and hence forecastability) in asset return signs, and dependence (and hence forecastability) in asset return volatilities. We show that they are very much interrelated, and we explore the relationships in detail. Among other things, we show that: (a) Volatility dependence produces sign dependence, so long as expected returns are nonzero, so that one should expect sign dependence, given the overwhelming evidence of volatility dependence; (b) The standard finding of little or no conditional mean dependence is entirely consistent with a significant degree of sign dependence and volatility dependence; (c) Sign dependence is not likely to be found via analysis of sign autocorrelations, runs tests, or traditional market timing tests, because of the special nonlinear nature of sign dependence; (d) Sign dependence is not likely to be found in very highfrequency (e.g., daily) or very lowfrequency (e.g., annual) returns; instead, it is more likely to be found at intermediate return horizons; (e) Sign dependence is very much present in actual U.S. equity returns, and its properties match closely our theoretical predictions; (f) The link between volatility forecastability and sign forecastability remains intact in conditionally nonGaussian environments, as for example with timevarying conditional skewness and/or kurtosis. Download Paper


97020 
Peter F. Christoffersen Francis X. Diebold 
"Optimal Prediction Under Asymmetric Loss"  
Prediction problems involving asymmetric loss functions arise routinely in many fields, yet the theory of optimal prediction under asymmetric loss is not well developed. We study the optimal prediction problem under general loss structures and characterize the optimal predictor. We compute the optimal predictor analytically in two leading cases. Analytic solutions for the optimal predictor are not available in more complicated cases, so we develop numerical procedures for computing it. We illustrate the results by forecasting the GARCH(1,1) process which, although white noise, is nontrivially forecastable under asymmetric loss. Download Paper


97017 
Peter F. Christoffersen Francis X. Diebold 
"Cointegration and LongHorizon Forecasting"  
It is widely believed that imposing cointegration on a forecasting system, if cointegration is in fact present, will improve longhorizon forecasts. Contrary to this belief, we show that at long horizons nothing is lost by ignoring cointegration when the forecasts are evaluated using standard multivariate forecast accuracy measures. In fact, simple univariate BoxJenkins forecasts are just as accurate. Our results highlight a potentially important deficiency of standard forecast accuracy measures  they fail to value the maintenance of cointegrating relationships among variables  and we suggest alternatives that explicitly do so. Download Paper
