Correcting the Errors: A Note on Volatility Forecast Evaluation Based on High-Frequency Data and Realized Volatilities

This note develops general model-free adjustment procedures for the calculation of unbiased volatility loss functions based on practically feasible realized volatility benchmarks. The procedures, which exploit the recent asymptotic distributional results in Barndorff-Nielsen and Shephard (2002a), are both easy-to-implement and highly accurate in empirically realistic situations. On properly accounting for the measurement errors in the volatility forecast evaluations reported in Andersen, Bollerslev, Diebold and Labys (2003), the adjustments result in markedly higher estimates for the true degree of return-volatility predictability. Cette note développe des méthodes d'ajustement, sans spécifier le modèle, qui corrigent le biais induit par les erreurs de mesures de la volatilité dans la mesure de performance des méthodes de prévision de la volatilité. Les procédures, qui utilisent la récente théorie asymptotique de Barndorff-Nielsen et Shephard (2002a), sont faciles à mettre en ?uvre et très performantes dans les situations empiriques usuelles. En particulier, la prise en compte des erreurs de mesures dans les procédures de prévision de Andersen, Bollerslev, Diebold et Labys (2003), amène à des performances de prévision de la volatilité très élevées.Measurement errors; model-free adjustment procedures; integrated volatility; realized volatility; high-frequency data; time series forecasting; Mincer-Zarnowitz regressions, Erreurs de mesure; méthode d'ajustement; volatilité intégrée, volatilité réalisée; données à haute fréquence; prévision de série chronologiques; régressions de Mincer-Zarnowitz

Sources of Uncertainty for Conducting Monetary Policy in Chile

This paper analyzes the quantitative relevance of additive, multiplicative and data uncertainty in the implementation of Chile’s monetary policy. For the analysis of data uncertainty, we focus on the uncertainty associated with the estimation of the output gap using real-time data and various well-known methods to estimate the output trend. We find that the revisions to the output gap are important and persistent and that the unobserved components method performs better with real-time data than with others more commonly used, like the HP filter. In the case of additive and multiplicative uncertainties, we estimate the equations that govern the behavior of the economy with time-varying parameters and with state-dependent variances in the shocks of the model. This allows us to analyze the contribution of these two types of uncertainty on the total uncertainty. We find that additive uncertainty is the most relevant to explain total uncertainty and that shocks to the model are state-dependent.

Modelling dynamic portfolio risk using risk drivers of elliptical processes

The situation of a limited availability of historical data is frequently encountered in portfolio risk estimation, especially in credit risk estimation. This makes it, for example, difficult to find temporal structures with statistical significance in the data on the single asset level. By contrast, there is often a broader availability of cross-sectional data, i.e., a large number of assets in the portfolio. This paper proposes a stochastic dynamic model which takes this situation into account. The modelling framework is based on multivariate elliptical processes which model portfolio risk via sub-portfolio specific volatility indices called portfolio risk drivers. The dynamics of the risk drivers are modelled by multiplicative error models (MEM) - as introduced by Engle (2002) - or by traditional ARMA models. The model is calibrated to Moody's KMV Credit Monitor asset returns (also known as firm-value returns) given on a monthly basis for 756 listed European companies at 115 time points from 1996 to 2005. This database is used by financial institutions to assess the credit quality of firms. The proposed risk drivers capture the volatility structure of asset returns in different industry sectors. A characteristic temporal structure of the risk drivers, cyclical as well as a seasonal, is found across all industry sectors. In addition, each risk driver exhibits idiosyncratic developments. We also identify correlations between the risk drivers and selected macroeconomic variables. These findings may improve the estimation of risk measures such as the (portfolio) Value at Risk. The proposed methods are general and can be applied to any series of multivariate asset or equity returns in finance and insurance. --Portfolio risk modelling,Elliptical processes,Credit risk,multiplicative error model,volatility clustering

A Mixture Multiplicative Error Model for Realized Volatility

A multiplicative error model with time-varying parameters and an error term following a mixture of gamma distributions is introduced. The model is fitted to the daily realized volatility series of Deutschemark/Dollar and Yen/Dollar returns and is shown to capture the conditional distribution of these variables better than the commonly used ARFIMA model. The forecasting performance of the new model is found to be, in general, superior to that of the set of volatility models recently considered by Andersen et al. (2003) for the same data.Mixture model, Realized volatility, Gamma distribution