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54
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 150 (17 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.
Separating microstructure noise from volatility
, 2006
"... There are two variance components embedded in the returns constructed using high frequency asset prices: the timevarying variance of the unobservable efficient returns that would prevail in a frictionless economy and the variance of the equally unobservable microstructure noise. Using sample moment ..."
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Cited by 64 (5 self)
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There are two variance components embedded in the returns constructed using high frequency asset prices: the timevarying 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 volatilitytiming trading strategy, we show that careful (optimal) separation of the two volatility components of the observed stock returns yields substantial utility gains.
Variation, jumps, market frictions and high frequency data in financial econometrics
, 2005
"... ..."
Inference for Continuous Semimartingales Observed at High Frequency: A General Approach
, 2008
"... The econometric literature of high frequency data often relies on moment estimators which are derived from assuming local constancy of volatility and related quantities. We here study this localconstancy approximation as a general approach to estimation in such data. We show that the technique yiel ..."
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Cited by 22 (8 self)
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The econometric literature of high frequency data often relies on moment estimators which are derived from assuming local constancy of volatility and related quantities. We here study this localconstancy approximation as a general approach to estimation in such data. We show that the technique yields asymptotic properties (consistency, normality) that are correct subject to an ex post adjustment involving asymptotic likelihood ratios. These adjustments are given. Several examples of estimation are provided: powers of volatility, leverage effect, integrated betas, bipower, and covariance under asynchronous observation. The first order approximations in this study can be over the period of one observation, or over blocks of successive observations. The advantage of blocking is a gain in transparency in defining and analyzing estimators. The theory relies heavily on the interplay between stable convergence and measure change, and on asymptotic expansions for martingales.
Lévydriven and fractionally integrated ARMA processes with continuous time parameter
 Statist. Sinica
"... The de nition and properties of Levydriven CARMA (continuoustime ARMA) processes are reviewed. Gaussian CARMA processes are special cases in which the driving Levy process is Brownian motion. The use of more general Levy processes permits the speci cation of CARMA processes with a wide variety ofm ..."
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Cited by 20 (2 self)
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The de nition and properties of Levydriven CARMA (continuoustime ARMA) processes are reviewed. Gaussian CARMA processes are special cases in which the driving Levy process is Brownian motion. The use of more general Levy processes permits the speci cation of CARMA processes with a wide variety ofmarginal distributions which may be asymmetric and heavier tailed than Gaussian. Nonnegative CARMA processes are of special interest, partly because of the introduction by BarndorNielsen and Shephard (2001) of nonnegativeLevydriven OrnsteinUhlenbeck processes as models for stochastic volatility. Replacing the OrnsteinUhlenbeck process byaLevydriven CARMA process with nonnegative kernel permits the modelling of nonnegative, heavytailed processes with a considerably larger range of autocovariance functions than is possible in the OrnsteinUhlenbeck framework. We also de ne a class of zeromean fractionally integrated Levydriven CARMA processes, obtained by convoluting the CARMA kernel with a kernel corresponding to RiemannLiouville fractional integration, and derive explicit expressions for the kernel and autocovariance functions of these processes. They are longmemory in the sense that their kernel and autocovariance functions decay asymptotically at hyperbolic rates depending on the order of fractional integration. In order to introduce longmemory into nonnegative Levydriven CARMA processes we replace the fractional integration kernel with a closely related absolutely integrable kernel. This gives a class of stationary nonnegative continuoustime Levydriven processes whose autocovariance functions at lag h also converge to zero at asymptotically hyperbolic rates.
Impact of Jumps on Returns and Realised Variances: Econometric analysis of timedeformed Lévy processes
 Journal of Econometrics
, 2004
"... In order to assess the e#ect of jumps on realised variance calculations, we study some of the econometric properties of timechanged Levy processes. We show that in general realised variance is an inconsistent estimator of the timechange, however we can derive the second order properties of real ..."
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Cited by 13 (11 self)
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In order to assess the e#ect of jumps on realised variance calculations, we study some of the econometric properties of timechanged Levy processes. We show that in general realised variance is an inconsistent estimator of the timechange, however we can derive the second order properties of realised variances and use these to estimate the parameters of such models. Our analytic results give a first indication of the degrees of inconsistency of realised variance as an estimator of the timechange in the nonBrownian case. Further, our results suggest volatility is even more predictable than has been shown by the recent econometric work on realised variance.
Stochastic Volatility
, 2005
"... Stochastic volatility (SV) is the main concept used in the fields of financial economics and mathematical finance to deal with the endemic timevarying volatility and codependence found in financial markets. Such dependence has been known for a long time, early comments include Mandelbrot (1963) and ..."
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Cited by 12 (0 self)
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Stochastic volatility (SV) is the main concept used in the fields of financial economics and mathematical finance to deal with the endemic timevarying volatility and codependence found in financial markets. Such dependence has been known for a long time, early comments include Mandelbrot (1963) and Officer (1973). It was also clear to the founding fathers of modern continuous time finance that homogeneity was an unrealistic if convenient simplification, e.g. Black and Scholes (1972, p. 416) wrote “... there is evidence of nonstationarity in the variance. More work must be done to predict variances using the information available. ” Heterogeneity has deep implications for the theory and practice of financial economics and econometrics. In particular, asset pricing theory is dominated by the idea that higher rewards may be expected when we face higher risks, but these risks change through time in complicated ways. Some of the changes in the level of risk can be modelled stochastically, where the level of volatility and degree of codependence between assets is allowed to change over time. Such models allow us to explain, for example, empirically observed departures from BlackScholesMerton prices for options and understand why we should expect to see occasional dramatic moves in financial markets. The outline of this article is as follows. In section 2 I will trace the origins of SV and provide links with the basic models used today in the literature. In section 3 I will briefly discuss some of the innovations in the second generation of SV models. In section 4 I will briefly discuss the literature on conducting inference for SV models. In section 5 I will talk about the use of SV to price options. In section 6 I will consider the connection of SV with realised volatility. A extensive reviews of this literature is given in Shephard (2005). 2 The origin of SV models The origins of SV are messy, I will give five accounts, which attribute the subject to different sets of people.
Fractional integral equations and state space transforms
 Bernoulli
"... We introduce a class of stochastic differential equations driven by fractional Brownian motion (FBM), which allow for a constructive method in order to obtain stationary solutions. This leads to a substantial extention of fractional OrnsteinUhlenbeck processes. Structural properties of this class o ..."
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Cited by 8 (1 self)
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We introduce a class of stochastic differential equations driven by fractional Brownian motion (FBM), which allow for a constructive method in order to obtain stationary solutions. This leads to a substantial extention of fractional OrnsteinUhlenbeck processes. Structural properties of this class of new models are investigated. Their stationary densities are given explicitly.