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92
Bayesian Analysis of Stochastic Volatility Models
, 1994
"... this article is to develop new methods for inference and prediction in a simple class of stochastic volatility models in which logarithm of conditional volatility follows an autoregressive (AR) times series model. Unlike the autoregressive conditional heteroscedasticity (ARCH) and gener alized ARCH ..."
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Cited by 371 (21 self)
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this article is to develop new methods for inference and prediction in a simple class of stochastic volatility models in which logarithm of conditional volatility follows an autoregressive (AR) times series model. Unlike the autoregressive conditional heteroscedasticity (ARCH) and gener alized ARCH (GARCH) models [see Bollerslev, Chou, and Kroner (1992) for a survey of ARCH modeling], both the mean and logvolatility equations have separate error terms. The ease of evaluating the ARCH likelihood function and the ability of the ARCH specification to accommodate the timevarying volatility found in many economic time series has fostered an explosion in the use of ARCH models. On the other hand, the likelihood function for stochastic volatility models is difficult to evaluate, and hence these models have had limited empirical application
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 265 (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...
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.
Using Daily Range Data to Calibrate Volatility Diffusions and Extract the Forward Integrated Variance
, 1999
"... 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 BlackScholes price with the forward integrated variance replacing the BlackScholes va ..."
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Cited by 64 (3 self)
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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 BlackScholes price with the forward integrated variance replacing the BlackScholes 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 closetoclose 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 longmemory 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...
Herd Behavior and Aggregate Fluctuations in Financial Markets
"... We present a simple model of a stock market where a random communication structure between agents generically gives rise to heavy tails in the distribution of stock price variations in the form of an exponentially truncated powerlaw, similar to distributions observed in recent empirical studies of ..."
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Cited by 50 (1 self)
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We present a simple model of a stock market where a random communication structure between agents generically gives rise to heavy tails in the distribution of stock price variations in the form of an exponentially truncated powerlaw, similar to distributions observed in recent empirical studies of high frequency market data. Our model provides a link between two wellknown market phenomena: the heavy tails observed in the distribution of stock market returns on one hand and 'herding' behavior in financial markets on the other hand. In particular, our study suggests a relation between the excess kurtosis observed in asset returns, the market order flow and the tendency of market participants to imitate each other. Keywords: heavy tails, financial markets, herd behavior, market organization, intermittency, random graphs, percolation. JEL Classification number: C0, D49, G19 1 R. Cont gratefully acknowledges an AMX fellowship from Ecole Polytechnique (France) and thanks Science & Financ...
Expected stock returns and variance risk premia, working paper
, 2008
"... Motivated by the implications from a stylized selfcontained general equilibrium model incorporating the effects of timevarying economic uncertainty, we show that the difference between implied and realized variation, or the variance risk premium, is able to explain a nontrivial fraction of the ti ..."
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Cited by 47 (1 self)
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Motivated by the implications from a stylized selfcontained general equilibrium model incorporating the effects of timevarying economic uncertainty, we show that the difference between implied and realized variation, or the variance risk premium, is able to explain a nontrivial fraction of the time series variation in post 1990 aggregate stock market returns, with high (low) premia predicting high (low) future returns. Our empirical results depend crucially on the use of “modelfree, ” as opposed to BlackScholes, options implied volatilities, along with accurate realized variation measures constructed from highfrequency intraday, as opposed to daily, data. The magnitude of the predictability is particularly striking at the intermediate quarterly return horizon, where it easily dominates that afforded by other popular predictor variables, like the P/E ratio, the default spread, and the consumptionwealth ratio (CAY).
Interdisciplinary application of nonlinear time series methods
 Phys. Reports
, 1998
"... This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely deterministic and the potential that remains in this situatio ..."
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Cited by 42 (5 self)
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This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely deterministic and the potential that remains in this situation is discussed. For signals with weakly nonlinear structure, the presence of nonlinearity in a general sense has to be inferred statistically. The paper reviews the relevant methods and discusses the implications for deterministic modeling. Most field measurements yield nonstationary time series, which poses a severe problem for their analysis. Recent progress in the detection and understanding of nonstationarity is reported. If a clear signature of approximate determinism is found, the notions of phase space, attractors, invariant manifolds etc. provide a convenient framework for time series analysis. Although the results have to be interpreted with great care, superior performance can be achieved for typical signal processing tasks. In particular, prediction and filtering of signals are discussed, as well as the classification of system states by means of time series recordings.
A new approach to international arbitrage pricing
 Journal of Finance
, 1993
"... us, seminar participants at the 1992 Econometric Society summer meeting in ..."
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Cited by 38 (3 self)
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us, seminar participants at the 1992 Econometric Society summer meeting in