Torben G. Andersen

Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts

A voluminous literature has emerged for modeling the temporal dependencies in financial market volatility using ARCH and stochastic volatility models. While most of these studies have documented highly significant in-sample parameter estimates and pronounced intertemporal volatility persistence, traditional ex post forecast evaluation criteria suggest that the models provide seemingly poor volatility forecasts. Contrary to this contention, the authors show that volatility models produce strikingly accurate interdaily forecasts for the latent volatility factor that would be of interest in most financial applications. New methods for improved ex post interdaily volatility measurements based on high-frequency intradaily data are also discussed. Copyright 1998 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

The distribution of realized stock return volatility

Abstract We examine “realized” daily equity return volatilities and correlations obtained from high-frequency intraday transaction prices on individual stocks in the Dow Jones Industrial Average. We find that the unconditional distributions of realized variances and covariances are highly right-skewed, while the realized logarithmic standard deviations and correlations are approximately Gaussian, as are the distributions of the returns scaled by realized standard deviations. Realized volatilities and correlations show strong temporal dependence and appear to be well described by long-memory processes. Finally, there is strong evidence that realized volatilities and correlations move together in a manner broadly consistent with latent factor structure.

The Distribution of Realized Exchange Rate Volatility

Using high-frequency data on deutschemark and yen returns against the dollar, we construct model-free estimates of daily exchange rate volatility and correlation that cover an entire decade. Our estimates, termed realized volatilities and correlations, are not only model-free, 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 normality-inducing volatility transformation, high contemporaneous correlation across volatilities, high correlation between correlation and volatilities, pronounced and persistent dynamics in volatilities and correlations, evidence of long-memory dynamics in volatilities and correlations, and remarkably precise scaling laws under temporal aggregation.

Intraday periodicity and volatility persistence in financial markets

Abstract The pervasive intraday periodicity in the return volatility in foreign exchange and equity markets is shown to have a strong impact on the dynamic properties of high frequency returns. Only by taking account of this strong intraday periodicity is it possible to uncover the complex intraday volatility dynamics that exists both within and across different financial markets. The explicit periodic modeling procedure developed here provides such a framework and thus sets the stage for a formal integration of standard volatility models with market microstructure variables to allow for a more comprehensive empirical investigation of the fundamental determinants behind the volatility clustering phenomenon.

Deutsche Mark-Dollar Volatility: Intraday Activity Patterns, Macroeconomic Announcements, and Longer Run Dependencies

This paper characterizes the volatility in the DM-dollar foreign exchange market using an annual sample of five-minute returns. Our modeling approach explicitly captures the pronounced intraday activity patterns, the strong macroeconomic announcement effects, and the volatility persistence, or ARCH effects, familiar from lower frequency returns. The different features are separately quantified and shown, in conjunction, to account for a substantial fraction of the realized return variability, both at the intradaily and daily levels. Moreover, we demonstrate how the high frequency returns, when properly modeled, constitute an extremely valuable and vastly underutilized resource for better understanding the volatility dynamics at the daily or lower frequencies.

Roughing it Up: Including Jump Components in the Measurement, Modeling and Forecasting of Return Volatility

A growing literature documents important gains in asset return volatility forecasting via use of realized variation measures constructed from high-frequency returns. We progress by using newly developed bipower variation measures and corresponding nonparametric tests for jumps. Our empirical analyses of exchange rates, equity index returns, and bond yields suggest that the volatility jump component is both highly important and distinctly less persistent than the continuous component, and that separating the rough jump moves from the smooth continuous moves results in significant out-of-sample volatility forecast improvements. Moreover, many of the significant jumps are associated with specific macroeconomic news announcements.

An Empirical Investigation of Continuous-Time Equity Return Models

This paper extends the class of stochastic volatility diffusions for asset returns to encompass Poisson jumps of time-varying intensity. We find that any reasonably descriptive continuous-time model for equity-index returns must allow for discrete jumps as well as stochastic volatility with a pronounced negative relationship between return and volatility innovations. We also find that the dominant empirical characteristics of the return process appear to be priced by the option market. Our analysis indicates a general correspondence between the evidence extracted from daily equity-index returns and the stylized features of the corresponding options market prices.

Estimating continuous-time stochastic volatility models of the short-term interest rate

Abstract We obtain consistent parameter estimates of continuous-time stochastic volatility diffusions for the U.S. risk-free short-term interest rate, sampled weekly over 1954–1995, using the Efficient Method of Moments procedure of Gallant and Tauchen. The preferred model displays mean reversion and incorporates ‘level effects’ and stochastic volatility in the diffusion function. Extensive diagnostics indicate that the Cox-Ingersoll-Ross model with an added stochastic volatility factor provides a good characterization of the short rate process. Further, they suggest that recently proposed GARCH models fail to approximate the discrete-time short rate dynamics, while ‘Level-EGARCH’ models perform reasonably well.

GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study

We examine the properties of alternative GMM procedures for estimation of the lognormal stochastic autoregressive volatility model through a large scale Monte Carlo study. We demonstrate that there is a fundamental trade-off between the number of moments, or information, included in estimation and the quality, or precision, of the objective function used for estimation. We provide a fairly transparent characterization of the trade-off in the present model. Furthermore, a large sample approximation to the optimal weighting matrix is utilized to explore the impact of the weighting matrix for estimation, specification testing and inference procedures, and to obtain practical efficiency bounds for the given class of GMM estimators. The results provide guidelines for obtaining desirable finite sample properties through the choice of the appropriate estimation design, and although the findings are specific to the model, the conclusions are likely to apply to a wide range of settings characterized by strong conditional heteroskedasticity and correlation among the moments.

Handbook of financial time series

Recent Developments in GARCH Modeling.- An Introduction to Univariate GARCH Models.- Stationarity, Mixing, Distributional Properties and Moments of GARCH(p, q)#x2013 Processes.- ARCH(#x221E ) Models and Long Memory Properties.- A Tour in the Asymptotic Theory of GARCH Estimation.- Practical Issues in the Analysis of Univariate GARCH Models.- Semiparametric and Nonparametric ARCH Modeling.- Varying Coefficient GARCH Models.- Extreme Value Theory for GARCH Processes.- Multivariate GARCH Models.- Recent Developments in Stochastic Volatility Modeling.- Stochastic Volatility: Origins and Overview.- Probabilistic Properties of Stochastic Volatility Models.- Moment#x2013 Based Estimation of Stochastic Volatility Models.- Parameter Estimation and Practical Aspects of Modeling Stochastic Volatility.- Stochastic Volatility Models with Long Memory.- Extremes of Stochastic Volatility Models.- Multivariate Stochastic Volatility.- Topics in Continuous Time Processes.- An Overview of Asset-Price Models.- Ornstein-Uhlenbeck Processes and Extensions.- Jump-Type Levy Processes.- Levy-Driven Continuous-Time ARMA Processes.- Continuous Time Approximations to GARCH and Stochastic Volatility Models.- Maximum Likelihood and Gaussian Estimation of Continuous Time Models in Finance.- Parametric Inference for Discretely Sampled Stochastic Differential Equations.- Realized Volatility.- Estimating Volatility in the Presence of Market Microstructure Noise: A Review of the Theory and Practical Considerations.- Option Pricing.- An Overview of Interest Rate Theory.- Extremes of Continuous-Time Processes..- Topics in Cointegration and Unit Roots.- Cointegration: Overview and Development.- Time Series with Roots on or Near the Unit Circle.- Fractional Cointegration.- Special Topics - Risk.- Different Kinds of Risk.- Value-at-Risk Models.- Copula-Based Models for Financial Time Series.- Credit Risk Modeling.- Special Topics - Time Series Methods.- Evaluating Volatility and Correlation Forecasts.- Structural Breaks in Financial Time Series.- An Introduction to Regime Switching Time Series Models.- Model Selection.- Nonparametric Modeling in Financial Time Series.- Modelling Financial High Frequency Data Using Point Processes.- Special Topics - Simulation Based Methods.- Resampling and Subsampling for Financial Time Series.- Markov Chain Monte Carlo.- Particle Filtering.