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Robust Properties of Stock Return Tails
, 2008
"... This paper explores the tail features of daily stock returns. Recently developed versions of the Hill estimator are used to measure the extreme positive and negative returns for a small set of individual daily stocks covering the period of 1926 through 2004. The findings report many of the accepted ..."
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This paper explores the tail features of daily stock returns. Recently developed versions of the Hill estimator are used to measure the extreme positive and negative returns for a small set of individual daily stocks covering the period of 1926 through 2004. The findings report many of the accepted stylized facts about stock returns. Scaling exponents are reliably near 3, and generally stable over time and across positive and negative tails. A simple measure of tail behavior, the Gaussian crossing point, is introduced which gives further information on tail behavior including some intriguing results suggesting that positive tails may be fatter than negative ones.
Estimation of the instantaneous volatility
 Stat. Inference Stoch. Process
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Denmark Long Memory and Tail dependence in Trading Volume and Volatility †
, 2009
"... This paper investigates longrun dependencies of volatility and volume, supposing that are driven by the same informative process. Logrealized volatility and logvolume are characterized by upper and lower tail dependence, where the positive tail dependence is mainly due to the jump component. The ..."
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This paper investigates longrun dependencies of volatility and volume, supposing that are driven by the same informative process. Logrealized volatility and logvolume are characterized by upper and lower tail dependence, where the positive tail dependence is mainly due to the jump component. The possibility that volume and volatility are driven by a common fractionally integrated stochastic trend, as the Mixture Distribution Hypothesis prescribes, is rejected. We model the two series with a bivariate Fractionally Integrated VAR specification. The joint density is parameterized by means of with different copula functions, which provide flexibility in modeling the dependence in the extremes and are computationally convenient. Finally, we present a simulation exercise to validate the model.
Nonlinear Connections Between Realized Volatility and High/Low Range Information
, 2012
"... In this paper we look at the relationship between daily realized volatility estimates using intraday data and range based estimates using daily high/low price range information. Several classical range based volatility estimators are compared with nonlinear functional forms in mapping range based in ..."
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In this paper we look at the relationship between daily realized volatility estimates using intraday data and range based estimates using daily high/low price range information. Several classical range based volatility estimators are compared with nonlinear functional forms in mapping range based information onto realized volatility measures. We find that the older range based estimators can be improved by using more generalized nonlinear functions of the high/low range information. We show that these nonlinearities form an important piece of information for understanding the dynamics of prices at high frequencies. We also show that these improved volatility estimates can be used in forecasting future variances and risk measures, and improve on the typical range estimators.
Estimation of the instantaneous volatility and detection of volatility jumps
, 2008
"... Concerning price processes, the fact that the volatility is not constant has been observed for a long time. So we deal with models as dXt = µtdt + σtdWt where σ is a stochastic process. Recent works on volatility modeling suggest that we should incorporate jumps in the volatility process. Empirical ..."
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Concerning price processes, the fact that the volatility is not constant has been observed for a long time. So we deal with models as dXt = µtdt + σtdWt where σ is a stochastic process. Recent works on volatility modeling suggest that we should incorporate jumps in the volatility process. Empirical observations suggest that simultaneous jumps on the price and the volatility [8, 9] exist. The hypothesis that jumps occur simultaneously makes the problem of volatility jump detection reduced to the prices jump detection. But in case of this hypothesis failure, we try to work in this direction. Among others, we use Jacod and AitSahalia ’ recent work [3] giving estimators of cumulated volatility ∫ t 0 σs  pds for any p ≥ 2. This tool allows us to deliver an estimator of instantaneous volatility. Moreover we prove a central limit theorem for it. Obviously, such a theorem provides a confidence interval for the instantaneous volatility and leads us to a test of the jump existence hypothesis. For instance, we consider a simplest model having volatility jumps, when volatility is piecewise constant: σt = ∑Nt−1 i=0 σi1 [τi,τi+1[(t). The jump times are τi,i ≥ 1, and σi is a Fτimeasurable random variable. Another example is studied: σt = Yt  where (Yt) is a solution to a Lévy driven SDE, with suitable coefficients. 1