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25
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 ..."
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Cited by 544 (53 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 ..."
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Cited by 329 (28 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.
Roughing It Up: Including Jump Components in the Measurement, Modeling and Forecasting of Return Volatility
 REVIEW OF ECONOMICS AND STATISTICS, FORTHCOMING
, 2006
"... A rapidly growing literature has documented important improvements in financial return volatility measurement and forecasting via use of realized variation measures constructed from highfrequency returns coupled with simple modeling procedures. Building on recent theoretical results in BarndorffNi ..."
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Cited by 164 (10 self)
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A rapidly growing literature has documented important improvements in financial return volatility measurement and forecasting via use of realized variation measures constructed from highfrequency returns coupled with simple modeling procedures. Building on recent theoretical results in BarndorffNielsen and Shephard (2004a, 2005) for related bipower variation measures, the present paper provides a practical and robust framework for nonparametrically measuring the jump component in asset return volatility. In an application to the DM/ $ exchange rate, the S&P500 market index, and the 30year 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 nonjump 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 nonjump 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.
Exchange Rate Returns Standardized by Realized Volatility are (Nearly) Gaussian
, 1999
"... Introduction and Basic Ideas The prescriptions of modern financial risk management hinge critically on the associated characterization of the distribution of future returns (cf., Diebold, Gunther and Tay, 1998, and Diebold, Hahn and Tay, 1999). Because volatility persistence renders highfrequency ..."
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Cited by 67 (11 self)
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Introduction and Basic Ideas The prescriptions of modern financial risk management hinge critically on the associated characterization of the distribution of future returns (cf., Diebold, Gunther and Tay, 1998, and Diebold, Hahn and Tay, 1999). Because volatility persistence renders highfrequency returns temporally dependent (e.g., Bollerslev, Chou and Kroner, 1992), it is the conditional return distribution, and not the unconditional distribution, that is of relevance for risk management. This is especially true in highfrequency situations, such as monitoring and managing the risk associated with the daytoday operations of a trading desk, where volatility clustering is omnipresent. Exchange rate returns are wellknown to be unconditionally symmetric but highly leptokurtic. Standardized daily or weekly returns from ARCH and related stochastic volatility models also appear symmetric but leptokurtic; that is, the distributions are not only unconditionally, bu
An Econometric Model of the Yield Curve with Macroeconomic Jump Effects
, 2000
"... This paper develops an arbitragefree timeseries model of yields in continuous time that incorporates central bank policy. Policyrelated events, such as FOMC meetings and releases of macroeconomic news the Fed cares about, are modeled as jumps. The model introduces a class of linearquadratic jump ..."
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Cited by 61 (6 self)
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This paper develops an arbitragefree timeseries model of yields in continuous time that incorporates central bank policy. Policyrelated events, such as FOMC meetings and releases of macroeconomic news the Fed cares about, are modeled as jumps. The model introduces a class of linearquadratic jumpdiffusions as state variables, which allows for a wide variety of jump types but still leads to tractable solutions for bond prices. I estimate a version of this model with U.S. interest rates, the Federal Reserve’s target rate, and key macroeconomic aggregates. The estimated model improves bond pricing, especially at short maturities. The “snakeshape ” of the volatility curve is linked to monetary policy inertia. A new monetary policy shock series is obtained by assuming that the Fed reacts to information available right before the FOMC meeting. According to the estimated policy rule, the Fed is mainly reacting to information contained in the yieldcurve. Surprises in analyst forecasts turn out to be merely temporary components of macro variables, so that the “humpshaped” yield response to these surprises is not consistent with a Taylortype policy rule.
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 54 (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
Some Like it Smooth, and Some Like it Rough: Untangling Continuous and Jump Components in Measuring, Modeling, and Forecasting Asset Return Volatility
, 2003
"... A rapidly growing literature has documented important improvements in volatility measurement and forecasting performance through the use of realized volatilities constructed from highfrequency returns coupled with relatively simple reduced form time series modeling procedures. Building on recent th ..."
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Cited by 47 (5 self)
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A rapidly growing literature has documented important improvements in volatility measurement and forecasting performance through the use of realized volatilities constructed from highfrequency returns coupled with relatively simple reduced form time series modeling procedures. Building on recent theoretical results from BarndorffNielsen and Shephard (2003c) for related bipower variation measures involving the sum of highfrequency absolute returns, the present paper provides a practical framework for nonparametrically measuring the jump component in the realized volatility measurements. Exploiting these ideas for a decade of highfrequency fiveminute returns for the DM/ $ exchange rate, the S&P500 aggregate market index, and the 30year U.S. Treasury Bond, we find the jump components to be distinctly less persistent than the contribution to the overall return variability originating from the continuous sample path component of the price process. Explicitly including the jump measure as an additional explanatory variable in an easytoimplement reduced form model for the realized volatilities results in highly significant jump coefficient estimates at the daily, weekly and quarterly forecasts horizons. As such, our results hold promise for improved financial asset allocation, risk management, and derivatives pricing, by separate modeling, forecasting and pricing of the continuous and jump components of the total return variability.
A New Class of Stochastic Volatility Models with Jumps: Theory and Estimation
, 1999
"... The purpose of this paper is to propose a new class of jump diffusions which feature both stochastic volatility and random intensity jumps. Previous studies have focused primarily on pure jump processes with constant intensity and lognormal jumps or constant jump intensity combined with a one facto ..."
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Cited by 36 (5 self)
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The purpose of this paper is to propose a new class of jump diffusions which feature both stochastic volatility and random intensity jumps. Previous studies have focused primarily on pure jump processes with constant intensity and lognormal jumps or constant jump intensity combined with a one factor stochastic volatility model. We introduce several generalizations which can better accommodate several empirical features of returns data. In their most general form we introduce a class of processes which nests jumpdiffusions previously considered in empirical work and includes the arline class of random intensity models studied by Bates (1998) and Duffie, Pan and Singleton (1998) but also allows for nonarline random intensity jump components. We attain the generality of our specification through a generic Lévy process characterization of the jump component. The processes we introduce share the desirable feature with the arline class that they yield analytically tractable and explicit option pricing formula. The nonarline class of processes we study include specifications where the random intensity jump component depends on the size of the previous jump which represent an alternative to arline random intensity jump processes which feature correlation between the stochastic volatility and jump component. We also allow for and experiment with different empirical specifications of the jump size distributions. We use two types of data sets. One involves the S&P500 and the other comprises of 100 years of daily Dow Jones index. The former is a return series often used in the literature and allows us to compare our results with previous studies. The latter has the advantage to provide a long time series and enhances the possibility of estimating the jump component more precisel...
Financial asset returns, directionofchange forecasting and volatility dynamics
, 2003
"... informs doi 10.1287/mnsc.1060.0520 ..."