Showing papers by "Tim Bollerslev published in 2006"

Volatility and correlation forecasting

Abstract: 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 3-5 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.

Volatility and Correlation Forecasting

Abstract: 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 3-5 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.

Leverage and Volatility Feedback Effects in High-Frequency Data

Abstract: We examine the relationship between volatility and past and future returns using high-frequency aggregate equity index data. Consistent with a prolonged ‘‘leverage’’ effect, we find the correlations between absolute high-frequency returns and current and past high-frequency returns to be significantly negative for several days, whereas the reverse cross-correlations are generally negligible. We also find that high-frequency data may be used in more accurately assessing volatility asymmetries over longer daily return horizons. Furthermore, our analysis of several popular continuous-time stochastic volatility models clearly points to the importance of allowing for multiple latent volatility factors for satisfactorily describing the observed volatility asymmetries.

Realized Beta: Persistence and Predictability

Abstract: A large literature over several decades reveals both extensive concern with the question of time-varying betas and an emerging consensus that betas are in fact time-varying, leading to the prominence of the conditional CAPM. Set against that background, we assess the dynamics in realized betas, vis-a-vis the dynamics in the underlying realized market variance and individual equity covariances with the market. Working in the recently popularized 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 fractionally integrated, 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.

Chapter 15 Volatility and Correlation Forecasting

Abstract: 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 3–5 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.

Realized Return Volatility, Asset Pricing, and Risk Management

Abstract: It is now widely accepted that expected returns, volatility, and broader financial risk measures all vary over time. In particular, there is a pronounced clustering in return volatility; occasional extreme return outliers--especially on the negative for equities; and an increase in return correlations during market downturns. This makes it more complicated for academics, regulators, and practitioners seeking to understand, monitor, act, and react to financial market dynamics to assess market conditions in real time. Textbook prescriptions for portfolio choice, asset pricing, and risk management typically are based on a static setting with known and invariant return distributions. These approaches are ill-suited for practical decision making: market agents know neither the parameters nor the parametric family of the return distribution, and the shape of the distribution is likely to change over time. Depending on the horizon, the challenges differ, with the notable exception that accurate assessment of the current volatility level remains pivotal. At daily or shorter intervals, it is critical also to understand the likely reaction of markets to impending news releases and to control for the intraday pattern in the market activity and return dynamics. For weekly and monthly frequencies, the persistence of volatility and the extent of asymmetry between return and volatility innovations both figure importantly in determining return distributions. For even longer quarterly and annual horizons, the main issues again relate to the temporal persistence of volatility, but good estimates of the non-negligible longer-run expected returns now also become critical. The increased availability of tick-by-tick financial trade records and real-time news reports, coupled with our enhanced capacity to store and process vast amounts of data, have led to important new insights in regards to the issues discussed above. Specifically, over the last few years a very active research agenda into the direct (model-free) measurement of the realized return variation and covariation of financial assets at daily or even higher intraday frequencies has developed. The intuition behind the realized volatility measure has been recognized for a while, albeit within a simplified setting. In a frictionless market with an unlimited set of price observations available over any interval, it is, quite generally, feasible to perfectly estimate instantaneous volatility if the process is not subject to jumps. However, given the discreteness of the price grid and other market microstructure effects, as well as the limited number of price observations available over short time intervals, even for liquid securities, instantaneous volatility cannot be measured with reasonable precision without (excessively) strong identifying assumptions. In the face of these practical limitations, we have focused a large part of our recent work on developing robust, yet accurate, volatility measures over nontrivial daily, or longer, time intervals that exploit the information available from intraday data. In so doing, it is important to recognize the main qualitative features that affect the intraday return process but are absent at daily and lower frequency levels. Most importantly, the intraday volatility pattern and the presence of outliers (jumps) render standard ARCH-type volatility models inadequate unless they are explicitly extended to accommodate such features. We show that the original studies applying standard modeling and inference techniques to the newly available intraday data were seriously mis-specified; they produced badly downward biased estimates of the degree of volatility persistence. (1) Meanwhile, by controlling for specific intraday features, we got much closer to the type of volatility dynamics obtained from daily data, although our model specification is still not entirely adequate. In short, direct estimation of the high-frequency volatility process is difficult and very sensitive to market microstructure effects and news. …

Expected Stock Returns and Variance Risk Premia

Abstract: Motivated by the implications from a stylized self-contained general equilibrium model incorporating the effects of time-varying economic uncertainty, we show that the difference between implied and realized variation, or the variance risk premium, is able to explain a non-trivial fraction of the time series variation in post 1990 aggregate stock market returns, with high (low) premia predicting high (low) future returns. Our empirical results depend crucially on the use of “model-free,” as opposed to Black-Scholes, options implied volatilities, along with accurate realized variation measures constructed from high-frequency intraday, as opposed to daily, data. The magnitude of the predictability is particularly strong at the intermediate quarterly return horizon, where it dominates that afforded by other popular predictor variables, like the P/E ratio, the default spread, and the consumption-wealth ratio (CAY).