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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 114 (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
Continuous Record Asymptotics for Rolling Sample Variance Estimators
 Econometrica
, 1996
"... It is widely known that conditional covariances of asset returns change over time. ..."
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Cited by 89 (0 self)
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It is widely known that conditional covariances of asset returns change over time.
Stock Volatility and the Crash of ‘87
 Review of Financial Studies
, 1990
"... STOCK VOLATILITY AND THE CRASH OF '87 This paper analyzes the behas br of stock return volatility using daily data from 1885 through 1987. The October 1987 stock market crash was unusual in many ways relative to prior history. In particular, stock volatility jumped dramatically during and after the ..."
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Cited by 65 (1 self)
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STOCK VOLATILITY AND THE CRASH OF '87 This paper analyzes the behas br of stock return volatility using daily data from 1885 through 1987. The October 1987 stock market crash was unusual in many ways relative to prior history. In particular, stock volatility jumped dramatically during and after the crash, but it returned to lower. more normal levels quickly. I use data on implied volatilities from call option prices and estimates of volatility from futures contracts on stock indexes to confirm this result.
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...
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
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News Arrival, Jump Dynamics, and Volatility Components for Individual Stock Returns
, 2003
"... This paper models components of the return distribution, which are assumed to be directed by a latent news process. The conditional variance of returns is a combination of jumps and smoothly changing components. A heterogeneous Poisson process with a timevarying conditional intensity parameter gove ..."
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Cited by 31 (2 self)
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This paper models components of the return distribution, which are assumed to be directed by a latent news process. The conditional variance of returns is a combination of jumps and smoothly changing components. A heterogeneous Poisson process with a timevarying conditional intensity parameter governs the likelihood of jumps. Unlike typical jump models with stochastic volatility, previous realizations of both jump and normal innovations can feed back asymmetrically into expected volatility. This model improves forecasts of volatility, particularly after large changes in stock returns. We provide empirical evidence of the impact and feedback effects of jump versus normal return innovations, leverage effects, and the timeseries dynamics of jump clustering. THERE IS A WIDESPREAD PERCEPTION in the financial press that volatility of asset returns has been changing. The new economy is introducing more uncertainty. Indeed, it can be argued that volatility is being transferred from the economy at large into the financial markets, which bear the necessary adjustment shocks. 1
A NoArbitrage Approach to RangeBased Estimation of Return Covariances and Correlations
, 2003
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Implications of Nonlinear Dynamics for Financial Risk Management
 Journal of Financial and Quantitative Analysis
, 1993
"... This paper demonstrates that when log price changes are not IID, their conditional density may be more accurate than their unconditional density for describing short term behavior. Using the BDS test of independence and identical distribution, daily log price changes in four currency futures contrac ..."
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Cited by 20 (0 self)
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This paper demonstrates that when log price changes are not IID, their conditional density may be more accurate than their unconditional density for describing short term behavior. Using the BDS test of independence and identical distribution, daily log price changes in four currency futures contracts are found to be not IID. While there appears to be no predictable conditional mean changes, conditional variances are predictable, and can be described by an autoregressive volatility model. Furthermore, this autoregressive volatility model seems to capture all the departures from independence and identical distribution. Based on this model, daily log price changes are decomposed into a predictable part and an unpredictable part. The predictable part is described parametrically by the autoregressive volatility model. The unpredictable part can be modeled by an empirical density, either parametrically or nonparametrically. This twostep seminonparametric method yields a conditional density for daily log price changes, which has a number of uses in financial risk management. In particular, one can directly calculate the capital requirement needed to cover losses of a futures position over one trading day. One can also use simulation methods to calculate the capital requirement over longer holding periods. This conditional density provides different, and probably more accurate, capital requirements than the unconditional density. I.