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189
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 272 (34 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...
Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk
 THE JOURNAL OF FINANCE • VOL. LVI
, 2001
"... This paper uses a disaggregated approach to study the volatility of common stocks at the market, industry, and firm levels. Over the period 1962–1997 there has been a noticeable increase in firmlevel volatility relative to market volatility. Accordingly, correlations among individual stocks and the ..."
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Cited by 270 (13 self)
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This paper uses a disaggregated approach to study the volatility of common stocks at the market, industry, and firm levels. Over the period 1962–1997 there has been a noticeable increase in firmlevel volatility relative to market volatility. Accordingly, correlations among individual stocks and the explanatory power of the market model for a typical stock have declined, whereas the number of stocks needed to achieve a given level of diversification has increased. All the volatility measures move together countercyclically and help to predict GDP growth. Market volatility tends to lead the other volatility series. Factors that may be responsible for these findings are suggested.
Power and Bipower Variation with Stochastic Volatility and Jumps
, 2003
"... This paper shows that realised power variation and its extension we introduce here called realised bipower variation is somewhat robust to rare jumps. We show realised bipower variation estimates integrated variance in SV models  thus providing a model free and consistent alternative to realis ..."
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Cited by 152 (21 self)
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This paper shows that realised power variation and its extension we introduce here called realised bipower variation is somewhat robust to rare jumps. We show realised bipower variation estimates integrated variance in SV models  thus providing a model free and consistent alternative to realised variance. Its robustness property means that if we have an SV plus infrequent jumps process then the di#erence between realised variance and realised bipower variation estimates the quadratic variation of the jump component. This seems to be the first method which can divide up quadratic variation into its continuous and jump components. Various extensions are given. Proofs of special cases of these results are given.
An empirical investigation of continuoustime equity return models
 Journal of Finance
, 2002
"... This paper extends the class of stochastic volatility diffusions for asset returns to encompass Poisson jumps of timevarying intensity. We find that any reasonably descriptive continuoustime model for equityindex returns must allow for discrete jumps as well as stochastic volatility with a pronou ..."
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Cited by 137 (10 self)
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This paper extends the class of stochastic volatility diffusions for asset returns to encompass Poisson jumps of timevarying intensity. We find that any reasonably descriptive continuoustime model for equityindex returns must allow for discrete jumps as well as stochastic volatility with a pronounced negative relationship between return and volatility innovations. We also find that the dominant empirical characteristics of the return process appear to be priced by the option market. Our analysis indicates a general correspondence between the evidence extracted from daily equityindex returns and the stylized features of the corresponding options market prices. MUCH ASSET AND DERIVATIVE PRICING THEORY is based on diffusion models for primary securities. However, prescriptions for practical applications derived from these models typically produce disappointing results. A possible explanation could be that analytic formulas for pricing and hedging are available for only a limited set of continuoustime representations for asset returns
Rangebased estimation of stochastic volatility models
, 2002
"... We propose using the price range in the estimation of stochastic volatility models. We show theoretically, numerically, and empirically that rangebased volatility proxies are not only highly efficient, but also approximately Gaussian and robust to microstructure noise. Hence rangebased Gaussian qu ..."
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Cited by 117 (11 self)
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We propose using the price range in the estimation of stochastic volatility models. We show theoretically, numerically, and empirically that rangebased volatility proxies are not only highly efficient, but also approximately Gaussian and robust to microstructure noise. Hence rangebased Gaussian quasimaximum likelihood estimation produces highly efficient estimates of stochastic volatility models and extractions of latent volatility. We use our method to examine the dynamics of daily exchange rate volatility and find the evidence points strongly toward twofactor models with one highly persistent factor and one quickly meanreverting factor. VOLATILITY IS A CENTRAL CONCEPT in finance, whether in asset pricing, portfolio choice, or risk management. Not long ago, theoretical models routinely assumed constant volatility ~e.g., Merton ~1969!, Black and Scholes ~1973!!. Today, however, we widely acknowledge that volatility is both time varying and predictable ~e.g., Andersen and Bollerslev ~1997!!, andstochastic volatility models are commonplace. Discrete and continuoustime stochastic volatility models are extensively used in theoretical finance, empirical finance, and financial econometrics, both in academe and industry ~e.g., Hull and
MULTIVARIATE GARCH MODELS: A SURVEY
"... This paper surveys the most important developments in multivariate ARCHtype modelling. It reviews the model specifications and inference methods, and identifies likely directions of future research. ..."
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Cited by 109 (7 self)
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This paper surveys the most important developments in multivariate ARCHtype modelling. It reviews the model specifications and inference methods, and identifies likely directions of future research.
Numerical Techniques for Maximum Likelihood Estimation of ContinuousTime Diffusion Processes
 JOURNAL OF BUSINESS AND ECONOMIC STATISTICS
, 2001
"... Stochastic differential equations often provide a convenient way to describe the dynamics of economic and financial data, and a great deal of effort has been expended searching for efficient ways to estimate models based on them. Maximum likelihood is typically the estimator of choice; however, sinc ..."
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Cited by 87 (0 self)
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Stochastic differential equations often provide a convenient way to describe the dynamics of economic and financial data, and a great deal of effort has been expended searching for efficient ways to estimate models based on them. Maximum likelihood is typically the estimator of choice; however, since the transition density is generally unknown, one is forced to approximate it. The simulationbased approach suggested by Pedersen (1995) has great theoretical appeal, but previously available implementations have been computationally costly. We examine a variety of numerical techniques designed to improve the performance of this approach. Synthetic data generated by a CIR model with parameters calibrated to match monthly observations of the U.S. shortterm interest rate are used as a test case. Since the likelihood function of this process is known, the quality of the approximations can be easily evaluated. On data sets with 1000 observations, we are able to approximate the maximum likelihood estimator with negligible error in well under one minute. This represents something on the order of a 10,000fold reduction in computational effort as compared to implementations without these enhancements. With other parameter settings designed to stress the methodology, performance remains strong. These ideas are easily generalized to multivariate settings and (with some additional work) to latent variable models. To illustrate, we estimate a simple stochastic volatility model of the U.S. shortterm interest rate.
Estimation of Stochastic Volatility Models with Diagnostics
 Journal of Econometrics
, 1995
"... Efficient Method of Moments (EMM) is used to fit the standard stochastic volatility model and various extensions to several daily financial time series. EMM matches to the score of a model determined by data analysis called the score generator. Discrepancies reveal characteristics of data that stoch ..."
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Cited by 82 (9 self)
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Efficient Method of Moments (EMM) is used to fit the standard stochastic volatility model and various extensions to several daily financial time series. EMM matches to the score of a model determined by data analysis called the score generator. Discrepancies reveal characteristics of data that stochastic volatility models cannot approximate. The two score generators employed here are "Semiparametric ARCH" and "Nonlinear Nonparametric". With the first, the standard model is rejected, although some extensions are accepted. With the second, all versions are rejected. The extensions required for an adequate fit are so elaborate that nonparametric specifications are probably more convenient. Corresponding author: George Tauchen, Duke University, Department of Economics, Social Science Building, Box 90097, Durham NC 277080097 USA, phone 19196601812, FAX 19196848974, email get@tauchen.econ.duke.edu. 0 1 Introduction The stochastic volatility model has been proposed as a descripti...
A Study towards a Unified Approach to the Joint Estimation of Objective and Risk Neutral Measures for the Purpose of Options Valuation
, 1999
"... The purpose of this paper is to bridge two strands of the literature, one pertaining to the objectiveorphysical measure used to model the underlying asset and the other pertaining to the riskneutral measure used to price derivatives. We propose a generic procedure using simultaneously the fundame ..."
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Cited by 75 (4 self)
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The purpose of this paper is to bridge two strands of the literature, one pertaining to the objectiveorphysical measure used to model the underlying asset and the other pertaining to the riskneutral measure used to price derivatives. We propose a generic procedure using simultaneously the fundamental price S t and a set of option contracts ### I it # i=1;m # where m # 1 and # I it is the BlackScholes implied volatility.We use Heston's #1993# model as an example and appraise univariate and multivariate estimation of the model in terms of pricing and hedging performance. Our results, based on the S&P 500 index contract, show that the univariate approach only involving options by and large dominates. Abyproduct of this #nding is that we uncover a remarkably simple volatility extraction #lter based on a polynomial lag structure of implied volatilities. The bivariate approachinvolving both the fundamental and an option appears useful when the information from the cash market ...