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, we 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.

https://faculty.washington.edu/ezivot/econ589//////AndersenBollerslevIER1998.pdf

Answering the skeptics: yes, standard volatility models do provide accurate forecasts*

This paper provides a general framework for integration of high-frequency 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 high-frequency intraday returns, in contrast, permits the use of traditional time series procedures for modeling and forecasting. Building on the theory of continuous-time arbitrage-free 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 long-memory Gaussian vector autoregression for the logarithmic daily realized volatitilies perform admirably compared to popular daily ARCH and related models. Moreover, the vector autoregressive volatility forecast, coupled with a parametric lognormal-normal mixture distribution implied by the theoretically and empirically grounded assumption of normally distributed standardized returns, gives rise to well-calibrated density forecasts of future returns, and correspondingly accurate quintile 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.

Modeling and Forecasting Realized Volatility

This paper provides a general framework for integration of high-frequency 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 high-frequency intraday returns, in contrast, permits the use of traditional time series procedures for modeling and forecasting. Building on the theory of continuous-time arbitrage-free 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 long-memory 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 lognormal-normal mixture distribution implied by the theoretically and empirically grounded assumption of normally distributed standardized returns, gives rise to well-calibrated 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.

/pdf/modeling-and-forecasting-realized-volatility-2mqo5gygak.pdf

Modeling and forecasting realized volatility

A complete theory for evaluating interval forecasts has not been worked out to date. Most of the literature implicitly assumes homoskedastic errors even when this is clearly violated, and proceed by merely testing for correct unconditional coverage. Consequently, I set out to build a consistent framework for conditional interval forecast evaluation, which is crucial when higher-order moment dynamics are present. The new methodology is demonstrated in an application to the exchange rate forecasting procedures advocated in risk management.

Evaluating Interval Forecasts.

We test for asymmetry in a model of the dependence between the Deutsche mark and the yen, in the sense that a different degree of correlation is exhibited during joint appreciations against the U.S. dollar versus during joint depreciations. We consider an extension of the theory of copulas to allow for conditioning variables, and employ it to construct flexible models of the conditional dependence structure of these exchange rates. We find evidence that the mark‐dollar and yen‐dollar exchange rates are more correlated when they are depreciating against the dollar than when they are appreciating.

/pdf/modelling-asymmetric-exchange-rate-dependence-3ncll9uq7l.pdf

Modelling asymmetric exchange rate dependence

Density forecasting is increasingly more important and commonplace, forexample in financial risk management, yet little attention has been given to theevaluation of density forecasts. We develop a simple and operational frameworkfor density forecast evaluation. We illustrate the framework with adetailed application to density forecasting of asset returns in environments withtime-varying volatility. Finally, we discuss several extensions.

https://papers.ssrn.com/sol3/Delivery.cfm/2451_14779.pdf?abstractid=1290957

Evaluating Density Forecasts with Applications to Financial Risk Management

Density forecasting is increasingly more important and commonplace, for example in financial risk management, yet little attention has been given to the evaluation of density forecasts. The authors develop a simple and operational framework for density forecast evaluation. They illustrate the framework with a detailed application to density forecasting of asset returns in environments with time-varying volatility. Finally, the authors discuss several extensions. Copyright 1998 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

https://ink.library.smu.edu.sg/cgi/viewcontent.cgi?article=1068&context=soe_research

Evaluating density forecasts with applications to financial risk management

We propose methods for evaluating density forecasts. We focus primarily on methods" that are applicable regardless of the particular user's loss function. We illustrate the methods" with a detailed simulation example, and then we present an application to density forecasting of" daily stock market returns. We discuss extensions for improving suboptimal density forecasts multi-step-ahead density forecast evaluation, multivariate density forecast evaluation for structural change and its relationship to density forecasting, and density forecast evaluation" with known loss function.

Evaluating Density Forecasts

We propose methods for evaluating density forecasts. We focus primarily on methods that are applicable regardless of the particular user's loss function. We illustrate the methods with a detailed simulation example, and then we present an application to density forecasting of daily stock market returns. We discuss extensions for improving suboptimal density forecasts, multi-step-ahead density forecast evaluation, multivariate density forecast evaluation, monitoring for structural change and its relationship to density forecasting, and density forecast evaluation with known loss function.

/pdf/evaluating-density-forecasts-585mu69b2z.pdf

Todd A. Gunther

Papers

Evaluating Density Forecasts with Applications to Financial Risk Management

Evaluating density forecasts with applications to financial risk management

Evaluating Density Forecasts

Evaluating Density Forecasts