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


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


04028 
Torben G. Andersen Tim Bollerslev Francis X. Diebold Clara Vega 
"RealTime Price Discovery in Stock, Bond and Foreign Exchange Markets"  
We characterize the response of U.S., German and British stock, bond and foreign exchange markets to realtime U.S. macroeconomic news. Our analysis is based on a unique data set of high frequency futures returns for each of the markets. We find that news surprises produce conditional mean jumps; hence highfrequency stock, bond and exchange rate dynamics are linked to fundamentals. The details of the linkages are particularly intriguing as regards equity markets. We show that equity markets react differently to the same news depending on the state of the economy, with bad news having a positive impact during expansions and the traditionallyexpected negative impact during recessions. We rationalize this by temporal variation in the competing "cash flow" and "discount rate" effects for equity valuation. This finding helps explain the timevarying correlation between stock and bond returns, and the relatively small equity market news effect when averaged across expansions and recessions. Lastly, relying on the pronounced heteroskedasticity in the highfrequency data, we document important contemporaneous linkages across all markets and countries overandabove the direct news announcement effects. Download Paper


04018 
Torben G. Andersen Tim Bollerslev Francis X. Diebold Jin (Ginger) Wu 
"Realized Beta: Persistence and Predictability"  
A large literature over several decades reveals both extensive concern with the question of timevarying betas and an emerging consensus that betas are in fact timevarying, leading to the prominence of the conditional CAPM. Set against that background, we assess the dynamics in realized betas, visàvis the dynamics in the underlying realized market variance and individual equity covariances with the market. Working in the recentlypopularized framework of realized volatility, we are led to a framework of nonlinear fractional cointegration: although realized variances and covariances are very highly persistent and well approximated as fractionallyintegrated, realized betas, which are simple nonlinear functions of those realized variances and covariances, are less persistent and arguably best modeled as stationary I(0) processes. We conclude by drawing implications for asset pricing and portfolio management. Download Paper


03025 
Torben G. Andersen Tim Bollerslev Francis X. Diebold 
"Some Like it Smooth, and Some Like it Rough: Untangling Continuous and Jump Components in Measuring, Modeling, ..."  
A rapidly growing literature has documented important improvements in volatility measurement and forecasting performance through the use of realized volatilities constructed from high frequency returns coupled with relatively simple reducedform time series modeling procedures. Building on recent theoretical results from BarndorffNielsen and Shephard (2003c,d) for related bipower variation measures involving the sum of high frequency absolute returns, the present paper provides a practical framework for nonparametrically measuring the jump component in realized volatility measurements. Exploiting these ideas for a decade of highfrequency fiveminute returns for the DM/$ exchange rate, the S&P 500 market index, and the 30year U.S. Treasury bond yield, we find the jump component of the price process to be distinctly less persistent than the continuous sample path component. Explicitly including the jump measure as an additional explanatory variable in an easyto implement reduced form model for realized volatility results in highly significant jump coefficient estimates at the daily, weekly and quarterly forecast horizons. As such, our results hold promise for improved financial asset allocation, risk management, and derivatives pricing, by separate modeling, forecasting and pricing of the continuous and jump components of total return variability. Download Paper


02019 
Torben G. Andersen Tim Bollerslev Francis X. Diebold 
"Parametric and Nonparametric Volatility Measurement"  
Volatility has been one of the most active areas of research in empirical finance and time series econometrics during the past decade. This chapter provides a unified continuoustime, frictionless, noarbitrage framework for systematically categorizing the various volatility concepts, measurement procedures, and modeling procedures. We define three different volatility concepts: (i) the notional volatility corresponding to the expost samplepath return variability over a fixed time interval, (ii) the exante expected volatility over a fixed time interval, and (iii) the instantaneous volatility corresponding to the strength of the volatility process at a point in time. The parametric procedures rely on explicit functional form assumptions regarding the expected and/or instantaneous volatility. In the discretetime ARCH class of models, the expectations are formulated in terms of directly observable variables, while the discrete and continuoustime stochastic volatility models involve latent state variable(s). The nonparametric procedures are generally free from such functional form assumptions and hence afford estimates of notional volatility that are flexible yet consistent (as the sampling frequency of the underlying returns increases). The nonparametric procedures include ARCH filters and smoothers designed to measure the volatility over infinitesimally short horizons, as well as the recentlypopularized realized volatility measures for (nontrivial) fixedlength time intervals. Download Paper


02011 
Torben G. Andersen Tim Bollerslev Francis X. Diebold Clara Vega 
"Micro Effects of Macro Announcements: RealTime Price Discovery in Foreign Exchange"  
Using a new dataset consisting of six years of realtime exchange rate quotations, macroeconomic expectations, and macroeconomic realizations (announcements), we characterize the conditional means of U.S. dollar spot exchange rates versus German Mark, British Pound, Japanese Yen, Swiss Franc, and the Euro. In particular, we find that announcement surprises (that is, divergences between expectations and realizations, or "news") produce conditional mean jumps; hence highfrequency exchange rate dynamics are linked to fundamentals. The details of the linkage are intriguing and include announcement timing and sign effects. The sign effect refers to the fact that the market reacts to news in an asymmetric fashion: bad news has greater impact than good news, which we relate to recent theoretical work on information processing and price discovery. Download Paper


01008 
Torben G. Andersen Tim Bollerslev Francis X. Diebold Paul Labys 
"Exchange Rate Returns Standardized by Realized Volatility are (Nearly) Gaussian"  
The prescriptions of modern financial risk management hinge critically on the associated characterization of the distribution of future returns (cf., Diebold, Gunther and Tay, 1998, and Diebold, Hahn and Tay, 1999). Because volatility persistence renders highfrequency returns temporally dependent (e.g., Bollerslev, Chou and Kroner, 1992), it is the conditional return distribution, and not the unconditional distribution, that is of relevance for risk management. This is especially true in highfrequency situations, such as monitoring and managing the risk associated with the daytoday operations of a trading desk, where volatility clustering is omnipresent. Download Paper


01003 
Torben G. Andersen Tim Bollerslev Francis X. Diebold Paul Labys 
"The Distribution of Realized Exchange Rate Volatility"  
Using highfrequency data on Deutschemark and Yen returns against the dollar, we construct modelfree estimates of daily exchange rate volatility and correlation, covering an entire decade. Our estimates, termed realized volatilities and correlations, are not only modelfree, but also approximately free of measurement error under general conditions, which we discuss in detail. Hence, for practical purposes, we may treat the exchange rate volatilities and correlations as observed rather than latent. We do so, and we characterize their joint distribution, both unconditionally and conditionally. Noteworthy results include a simple normalityinducing volatility transformation, high contemporaneous correlation across volatilities, high correlation between correlation and volatilities, pronounced and persistent dynamics in volatilities and correlations, evidence of longmemory dynamics in volatilities and correlations, and remarkably precise scaling laws under temporal aggregation. Download Paper


01002 
Torben G. Andersen Tim Bollerslev Francis X. Diebold Paul Labys 
"Modeling and Forecasting Realized Volatility  
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This paper provides a general framework for integration of highfrequency intraday data into the measurement, modeling, and forecasting of daily and lower frequency volatility and return distributions. Most procedures for modeling and forecasting financial asset return volatilities, correlations, and distributions rely on restrictive and complicated parametric multivariate ARCH or stochastic volatility models, which often perform poorly at intraday frequencies. Use of realized volatility constructed from highfrequency intraday returns, in contrast, permits the use of traditional time series procedures for modeling and forecasting. Building on the theory of continuoustime arbitragefree price processes and the theory of quadratic variation, we formally develop the links between the conditional covariance matrix and the concept of realized volatility. Next, using continuously recorded observations for the Deutschemark / Dollar and Yen / Dollar spot exchange rates covering more than a decade, we find that forecasts from a simple longmemory Gaussian vector autoregression for the logarithmic daily realized volatilities perform admirably compared to popular daily ARCH and related models. Moreover, the vector autoregressive volatility forecast, coupled with a parametric lognormalnormal mixture distribution implied by the theoretically and empirically grounded assumption of normally distributed standardized returns, gives rise to wellcalibrated density forecasts of future returns, and correspondingly accurate quantile estimates. Our results hold promise for practical modeling and forecasting of the large covariance matrices relevant in asset pricing, asset allocation and financial risk management applications. Download Paper


01001 
Torben G. Andersen Tim Bollerslev Francis X. Diebold Heiko Ebens 
"The Distribution of Stock Return Volatility"  
We exploit direct modelfree measures of daily equity return volatility and correlation obtained from highfrequency intraday transaction prices on individual stocks in the Dow Jones Industrial Average over a fiveyear period to confirm, solidify and extend existing characterizations of stock return volatility and correlation. We find t hat t he unconditional distributions of the variances and covariances for all thirty stocks are leptokurtic and highly skewed to the right, while the logarithmic standard deviations and correlations all appear approximately Gaussian. Moreover, the distributions of the returns scaled by the realized standard deviations are also Gaussian. Consistent with our documentation of remarkably precise scaling laws under temporal aggregation, the realized logarithmic standard deviations and correlations all show strong temporal dependence and appear to be well described by longmemory processes. Positive returns have less impact on future variances and correlations than negative returns of the same absolute magnitude, although the economic importance of this asymmetry is minor. Finally, there is strong evidence that equity volatilities and correlations move together, possibly reducing the benefits to portfolio diversification when the market is most volatile. Our findings are broadly consistent with a latent volatility factor structure, and they set the stage for improved highdimensional volatility modeling and outofsample forecasting, which in turn hold promise for the development of better decision making in practical situations of risk management, portfolio allocation, and asset pricing. Download Paper
