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64
Modeling and Forecasting Realized Volatility
, 2002
"... 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 rightskewed, the distributions of the logarithms of realized volatilities are a ..."
Abstract

Cited by 479 (50 self)
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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 rightskewed, the distributions of the logarithms of realized volatilities are approximately Gaussian. Third, the longrun dynamics of realized logarithmic volatilities are well approximated by a fractionallyintegrated longmemory process. Motivated by the three ABDL empirical regularities, we proceed to estimate and evaluate a multivariate model for the logarithmic realized volatilities: a fractionallyintegrated 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 highfrequency 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 lognormalnormal mixture forecast distribution provides conditionally wellcalibrated 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 arbitragefree multivariate pricing environment. In section 3 we discuss the practical construction of realized volatilities from highfrequency foreign exchange returns. Next, in section 4 we summarize the salient distributional features of r...
The Distribution of Realized Exchange Rate Volatility
 Journal of the American Statistical Association
, 2001
"... Using highfrequency data on deutschemark and yen returns against the dollar, we construct modelfree estimates of daily exchange rate volatility and correlation that cover an entire decade. Our estimates, termed realized volatilities and correlations, are not only modelfree, but also approximately ..."
Abstract

Cited by 284 (26 self)
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Using highfrequency data on deutschemark and yen returns against the dollar, we construct modelfree estimates of daily exchange rate volatility and correlation that cover an entire decade. Our estimates, termed realized volatilities and correlations, are not only modelfree, 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 normalityinducing volatility transformation, high contemporaneous correlation across volatilities, high correlation between correlation and volatilities, pronounced and persistent dynamics in volatilities and correlations, evidence of longmemory dynamics in volatilities and correlations, and remarkably precise scaling laws under temporal aggregation.
The distribution of realized stock return volatility
, 2001
"... We examine "realized" daily equity return volatilities and correlations obtained from highfrequency intraday transaction prices on individual stocks in the Dow Jones ..."
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Cited by 211 (18 self)
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We examine "realized" daily equity return volatilities and correlations obtained from highfrequency intraday transaction prices on individual stocks in the Dow Jones
Econometric analysis of realized covariation: high frequency based covariance, regression, and correlation in financial economics
 Econometrica
, 2004
"... This paper analyses multivariate high frequency financial data using realized covariation. We provide a new asymptotic distribution theory for standard methods such as regression, correlation analysis, and covariance. It will be based on a fixed interval of time (e.g., a day or week), allowing the ..."
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Cited by 55 (0 self)
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This paper analyses multivariate high frequency financial data using realized covariation. We provide a new asymptotic distribution theory for standard methods such as regression, correlation analysis, and covariance. It will be based on a fixed interval of time (e.g., a day or week), allowing the number of high frequency returns during this period to go to infinity. Our analysis allows us to study how high frequency correlations, regressions, and covariances change through time. In particular we provide confidence intervals for each of these quantities.
Noarbitrage semimartingale restrictions for continuoustime volatility models subject to leveral effects, jumps and i.i.d. noise: Theory and testable distributional implications
 JOURNAL OF ECONOMETRICS
, 2007
"... We develop a sequential procedure to test the adequacy of jumpdiffusion models for return distributions. We rely on intraday data and nonparametric volatility measures, along with a new jump detection technique and appropriate conditional moment tests, for assessing the import of jumps and levera ..."
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Cited by 47 (9 self)
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We develop a sequential procedure to test the adequacy of jumpdiffusion models for return distributions. We rely on intraday data and nonparametric volatility measures, along with a new jump detection technique and appropriate conditional moment tests, for assessing the import of jumps and leverage effects. A novel robusttojumps approach is utilized to alleviate microstructure frictions for realized volatility estimation. Size and power of the procedure are explored through Monte Carlo methods. Our empirical findings support the jumpdiffusive representation for S&P500 futures returns but reveal
Variation, jumps, market frictions and high frequency data in financial econometrics
, 2005
"... ..."
Default risk and diversification: Theory and applications
 Mathematical Finance
, 2002
"... Recent advances in the theory of credit risk allow the use of standard term structure machinery for default risk modeling and estimation. The empirical literature in this area often interprets the drift adjustments of the default intensity’s diffusion state variables as the only default risk premium ..."
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Cited by 40 (7 self)
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Recent advances in the theory of credit risk allow the use of standard term structure machinery for default risk modeling and estimation. The empirical literature in this area often interprets the drift adjustments of the default intensity’s diffusion state variables as the only default risk premium. We show that this interpretation implies a restriction on the form of possible default risk premia, which can be justified through exact and approximate notions of “diversifiable default risk.” The equivalence between the empirical and martingale default intensities that follows from diversifiable default risk greatly facilitates the pricing and management of credit risk. We emphasize that this is not an equivalence in distribution, and illustrate its importance using credit spread dynamics estimated in Duffee (1999). We also argue that the assumption of diversifiability is implicitly used in certain existing models of mortgagebacked securities.