Volatility permeates modern financial theories and decision making processes. As such, accurate measures and good forecasts of future volatility are critical for the implementation and evaluation of asset and derivative pricing theories as well as trading and hedging strategies. In response to this, a voluminous literature has emerged for modeling the temporal dependencies in financial market volatility at the daily and lower frequencies using ARCH and stochastic volatility type models. Most of these studies find highly significant in-sample parameter estimates and pronounced intertemporal volatility persistence. Meanwhile, when judged by standard forecast evaluation criteria, based on the squared or absolute returns over daily or longer forecast horizons, standard volatility models provide seemingly poor forecasts. The present paper demonstrates that, contrary to this contention, in empirically realistic situations the models actually produce strikingly accurate interdaily forecasts f...

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this paper is built. First, although raw returns are clearly leptokurtic, returns standardized by realized volatilities are approximately Gaussian. Second, although the distributions of realized volatilities are clearly right-skewed, the distributions of the logarithms of realized volatilities are approximately Gaussian. Third, the long-run dynamics of realized logarithmic volatilities are well approximated by a fractionally-integrated long-memory process. Motivated by the three ABDL empirical regularities, we proceed to estimate and evaluate a multivariate model for the logarithmic realized volatilities: a fractionally-integrated Gaussian vector autoregression (VAR) . Importantly, our approach explicitly permits measurement errors in the realized volatilities. Comparing the resulting volatility forecasts to those obtained from currently popular daily volatility models and more complicated high-frequency models, we find that our simple Gaussian VAR forecasts generally produce superior forecasts. Furthermore, we show that, given the theoretically motivated and empirically plausible assumption of normally distributed returns conditional on the realized volatilities, the resulting lognormal-normal mixture forecast distribution provides conditionally well-calibrated density forecasts of returns, from which we obtain accurate estimates of conditional return quantiles. In the remainder of this paper, we proceed as follows. We begin in section 2 by formally developing the relevant quadratic variation theory within a standard frictionless arbitrage-free multivariate pricing environment. In section 3 we discuss the practical construction of realized volatilities from high-frequency foreign exchange returns. Next, in section 4 we summarize the salient distributional features of r...

Recent studies have suggested that stock markets' volatility has a type of long-range dependence that is not appropriately described by the usual Generalized Autoregressive Conditional Heteroskedastic (GARCH) and Exponential GARCH (EGARCH) models. In this paper, different models for describing this long-range dependence are examined and the properties of a Long-Memory Stochastic Volatility (LMSV) model, constructed by incorporating an Autoregressive Fractionally Integrated Moving Average (ARFIMA) process in a stochastic volatility scheme, are discussed. Strongly consistent estimators for the parameters of this LMSV model are obtained by maximizing the spectral likelihood. The distribution of the estimators is analyzed by means of a Monte Carlo study. The LMSV is applied to daily stock market returns providing an improved description of the volatility behavior. In order to assess the empirical relevance of this approach, tests for long-memory volatility are described and applied to an e...

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This paper surveys the most important developments in multivariate ARCH-type modelling. It reviews the model specifications and inference methods, and identifies likely directions of future research.

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A common model for security price dynamics is the continuous time stochastic volatility model. For this model, Hull and White (1987) show that the price of a derivative claim is the conditional expectation of the Black-Scholes price with the forward integrated variance replacing the Black-Scholes variance. Implementing the Hull and White characterization requires both estimates of the price dynamics and the conditional distribution of the forward integrated variance given observed variables. Using daily data on close-to-close price movement and the daily range, we find that standard models do not fit the data very well and a more general three factor model does better, as it mimics the long-memory feature of financial volatility. We develop techniques for estimating the conditional distribution of the forward integrated variance given observed variables. 1 Introduction This paper has two objectives: The first is to extend and implement methods for estimating diffusion models of secu...

A rapidly growing literature has documented important improvements in financial return volatility measurement and forecasting via use of realized variation measures constructed from high-frequency returns coupled with simple modeling procedures. Building on recent theoretical results in Barndorff-Nielsen and Shephard (2004a, 2005) for related bi-power variation measures, the present paper provides a practical and robust framework for non-parametrically measuring the jump component in asset return volatility. In an application to the DM/ $ exchange rate, the S&P500 market index, and the 30-year U.S. Treasury bond yield, we find that jumps are both highly prevalent and distinctly less persistent than the continuous sample path variation process. Moreover, many jumps appear directly associated with specific macroeconomic news announcements. Separating jump from non-jump movements in a simple but sophisticated volatility forecasting model, we find that almost all of the predictability in daily, weekly, and monthly return volatilities comes from the non-jump component. Our results thus set the stage for a number of interesting future econometric developments and important financial applications by separately modeling, forecasting, and pricing the continuous and jump components of the total return variation process.

There are two variance components embedded in the returns constructed using high frequency asset prices: the time-varying variance of the unobservable efficient returns that would prevail in a frictionless economy and the variance of the equally unobservable microstructure noise. Using sample moments of high frequency return data recorded at different frequencies, we provide a simple and robust technique to identify both variance components. In the context of a volatility-timing trading strategy, we show that careful (optimal) separation of the two volatility components of the observed stock returns yields substantial utility gains.