### Long

"... memory and power law coherency between realized volatility and trading volume ..."

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memory and power law coherency between realized volatility and trading volume

### Grasping Economic Jumps by Sparse Sampling Using Intradaily Highs and Lows

, 2010

"... Preliminary version, comments welcome Economic shocks like unexpected changes in federal funds rate typ-ically cause jumps in economic time series such as asset prices, indices or exchange rates. However, existing high-frequency methods to ex post measure and detect jumps fail to capture these econo ..."

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Preliminary version, comments welcome Economic shocks like unexpected changes in federal funds rate typ-ically cause jumps in economic time series such as asset prices, indices or exchange rates. However, existing high-frequency methods to ex post measure and detect jumps fail to capture these economic jumps. In this paper, we exploit the information embodied in intradaily highs and lows to develop new methods for disentangling volatility contribu-tions originating from diffusive price behaviour and economic jumps. Treating positive and negative jumps separately, we provide estimators and tests for diffusive volatility, positive and negative jumps. Empir-ically, we find more economic jumps than previously reported.

### The Impact of Jumps and Leverage in Forecasting Co-Volatility∗

, 2015

"... The paper investigates the impact of jumps in forecasting co-volatility, accommodating leverage effects. We modify the jump-robust two time scale covariance estimator of Boudt and Zhang (2013) such that the estimated matrix is positive definite. Using this approach we can disentangle the estimates o ..."

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The paper investigates the impact of jumps in forecasting co-volatility, accommodating leverage effects. We modify the jump-robust two time scale covariance estimator of Boudt and Zhang (2013) such that the estimated matrix is positive definite. Using this approach we can disentangle the estimates of the integrated co-volatility matrix and jump variations from the quadratic covariation matrix. Empirical results for three stocks traded on the New York Stock Exchange indicate that the co-jumps of two assets have a significant impact on future co-volatility, but that the impact is negligible for forecasting weekly and monthly horizons.

### Lombard Odier Investment Managers

, 2009

"... The estimation of the jump component in asset pricing has witnessed a considerably growing body of literature. Of particular interest is the decomposition of total volatility between its continuous and jump components. Recent contributions highlight the importance of the jump component in forecastin ..."

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The estimation of the jump component in asset pricing has witnessed a considerably growing body of literature. Of particular interest is the decomposition of total volatility between its continuous and jump components. Recent contributions highlight the importance of the jump component in forecasting the volatility at different horizons. In this paper, we extend the methodology developed by Maheu and McCurdy (2011) to measure the information content of intraday data in forecasting the density of returns at horizons up to 60 days. We extract jumps as in Andersen, Bollerslev, Frederiksen and Nielsen (2010) to have a measure of the jumps in returns. Then, we estimate a bivariate model of returns and volatilities where the jump component is independently modeled. Our empirical results for S&P 500 futures, WTI crude oil futures, and the USD/JPY exchange rate confirm the importance of

### Realized wavelet-based estimation of integrated variance and jumps in the presence of noise I

"... We introduce wavelet-based methodology for estimation of realized variance allowing its mea-surement in the time-frequency domain. Using smooth wavelets and Maximum Overlap Discrete Wavelet Transform, we allow for the decomposition of the realized variance into several investment horizons and jumps. ..."

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We introduce wavelet-based methodology for estimation of realized variance allowing its mea-surement in the time-frequency domain. Using smooth wavelets and Maximum Overlap Discrete Wavelet Transform, we allow for the decomposition of the realized variance into several investment horizons and jumps. Basing our estimator in the two-scale realized variance framework, we are able to utilize all available data and get feasible estimator in the presence of microstructure noise as well. The estimator is tested in a large numerical study of the finite sample performance and is compared to other popular realized variation estimators. We use different simulation settings with changing noise as well as jump level in different price processes including long memory fractional stochastic volatility model. The results reveal that our wavelet-based estimator is able to estimate and forecast the realized measures with the greatest precision. Our time-frequency estimators not only produce feasible estimates, but also decompose the realized variation into arbitrarily chosen investment horizons. We apply it to study the volatility of forex futures during the recent crisis at several investment horizons and obtain the results which provide us with better understanding of the volatility dynamics.

### RTAQ: Tools for the analysis of trades and quotes in R

, 2010

"... The Trades and Quotes data of the New York Stock Exchange is a popular input for the implementation of intraday trading strategies, the measurement of liquidity and volatility and investigation of the market microstructure, among others. This document describes a collection of R functions to careful ..."

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The Trades and Quotes data of the New York Stock Exchange is a popular input for the implementation of intraday trading strategies, the measurement of liquidity and volatility and investigation of the market microstructure, among others. This document describes a collection of R functions to carefully clean and match the trades and quotes data, cal-culate ex post liquidity and volatility measures and detect price jumps in the data.

### Bootstrapping high-frequency jump tests Prosper Dovonon

, 2014

"... In this paper, we consider bootstrap jump tests based on functions of realized volatility and bipower variation, as originally proposed by Barndor¤-Nielsen and Shephard (2006). Our aim is to improve the
nite sample size of the asymptotic theory-based tests while retaining good power. In order to do ..."

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In this paper, we consider bootstrap jump tests based on functions of realized volatility and bipower variation, as originally proposed by Barndor¤-Nielsen and Shephard (2006). Our aim is to improve the
nite sample size of the asymptotic theory-based tests while retaining good power. In order to do so, we generate the bootstrap observations under the null of no jumps, by drawing them randomly from a mean zero Gaussian distribution with a variance given by a local estimate of integrated volatility (which we call fv̂ni g). Our rst contribution is to give a set of high level conditions on fv̂ni g such that any bootstrap method of this form has the asymptotic correct size and is alternative-consistent. We then verify these high level conditions for a speci
c example of fv̂ni g based on the product of L multipowers of local realized volatility estimates, each of them computed over M consecutive non-overlapping intraday returns. We show that this choice satis
es our high level conditions under both the null and the alternative hypothesis of jumps when the maximum of the multipowers is strictly less than 1=2. This is equivalent to letting L> 2 when the multipowers are all equal to 1=L. When L 2; the bootstrap is able to mimic the null distribution only under the null of no jumps. In particular, we cannot guarantee that it is alternative-consistent when L = 1 and M = 1, which corresponds to the standard wild bootstrap based on a Gaussian external random variable. Our simulations con rm that this choice has very poor
nite sample properties. The simulations also show that by appropriately choosing M and L, we can greatly reduce the overrejections that are typically associated with the Barndor¤-Nielsen and Shephard (2006) tests without compromising power.

### Covariances and Correlations with non-synchronous prices

, 2014

"... We study the class of disentangled realized estimators for the integrated covariance matrix of Brownian semimartingales with finite activity jumps. These estimators separate correla-tions and volatilities. We analyze – in a thorough Monte Carlo study – different combinations of quantile-and-median-b ..."

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We study the class of disentangled realized estimators for the integrated covariance matrix of Brownian semimartingales with finite activity jumps. These estimators separate correla-tions and volatilities. We analyze – in a thorough Monte Carlo study – different combinations of quantile-and-median-based realized volatilities, and four estimators of realized correlations with three synchronization schemes. Their finite sample properties are studied under four data generating processes and in presence, or not, of microstructure noise, and under synchronous and asynchronous trading. The main finding is that pre-averaged disentangled estimators provide a precise, computationally efficient and easy alternative to measure integrated covari-ances on basis of noisy and asynchronous prices. Moreover, the gain is not only statistical but also financial. A minimum variance portfolio application shows the superiority of the disentangled realized estimators in terms of numerous performance metrics.