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54
Estimation of volatility functionals in the simultaneous presence of microstructure noise and jumps
, 2009
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Jump robust volatility estimation using nearest neighbor truncation
, 2009
"... We propose two new jumprobust estimators of integrated variance based on highfrequency return observations. These MinRV and MedRV estimators provide an attractive alternative to the prevailing bipower and multipower variation measures. Specifically, the MedRV estimator has better theoretical effic ..."
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Cited by 35 (3 self)
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We propose two new jumprobust estimators of integrated variance based on highfrequency return observations. These MinRV and MedRV estimators provide an attractive alternative to the prevailing bipower and multipower variation measures. Specifically, the MedRV estimator has better theoretical efficiency properties than the tripower variation measure and displays better finitesample robustness to both jumps and the occurrence of “zero” returns in the sample. Unlike the bipower variation measure the new estimator allows for the development of an asymptotic limit theory in the presence of jumps. Finally, it retains the local nature associated with the low order multipower variation measures. This proves essential for alleviating finite sample biases arising from the pronounced intraday volatility pattern which afflict alternative jumprobust estimators based on longer blocks of returns. An empirical investigation of the Dow Jones 30 stocks and an extensive simulation study corroborate the robustness and efficiency properties of the new estimators.
Threshold Bipower Variation and the Impact of Jumps on Volatility Forecasting
, 2010
"... This study reconsiders the role of jumps for volatility forecasting by showing that jumps have a positive and mostly significant impact on future volatility. This result becomes apparent once volatility is separated into its continuous and discontinuous component using estimators which are not only ..."
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Cited by 27 (6 self)
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This study reconsiders the role of jumps for volatility forecasting by showing that jumps have a positive and mostly significant impact on future volatility. This result becomes apparent once volatility is separated into its continuous and discontinuous component using estimators which are not only consistent, but also scarcely plagued by smallsample bias. To this purpose, we introduce the concept of threshold bipower variation, which is based on the joint use of bipower variation and threshold estimation. We show that its generalization (threshold multipower variation) admits a feasible central limit theorem in the presence of jumps and provides less biased estimates, with respect to the standard multipower variation, of the continuous quadratic variation in finite samples. We further provide a new test for jump detection which has substantially more power than tests based on multipower variation. Empirical analysis (on the S&P500 index, individual stocks and US bond yields) shows that the proposed techniques improve significantly the accuracy of volatility forecasts especially in periods following the occurrence of a jump.
Estimating Quadratic Variation when Quoted Prices Jump by a Constant Increment
"... For financial assets whose best quotes almost always change by jumping by one price tick (e.g. a penny), this paper proposes an estimator of Quadratic Variation which controls for microstructure effects. It compares the number of alternations, where quotes jump back to their previous price, to the n ..."
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Cited by 23 (2 self)
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For financial assets whose best quotes almost always change by jumping by one price tick (e.g. a penny), this paper proposes an estimator of Quadratic Variation which controls for microstructure effects. It compares the number of alternations, where quotes jump back to their previous price, to the number of other jumps. If quotes are found to exhibit “uncorrelated alternation”, the estimator is consistent in a limit theory where jumps are very frequent and small. This condition is checked across a range of markets, which is enlarged by suitably rounding prices. The estimator helps to forecast volatility. A multivariate extension and feasible asymptotic theory are developed.
Stochastic Volatility
, 2005
"... Stochastic volatility (SV) is the main concept used in the fields of financial economics and mathematical finance to deal with the endemic timevarying volatility and codependence found in financial markets. Such dependence has been known for a long time, early comments include Mandelbrot (1963) and ..."
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Cited by 21 (1 self)
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Stochastic volatility (SV) is the main concept used in the fields of financial economics and mathematical finance to deal with the endemic timevarying volatility and codependence found in financial markets. Such dependence has been known for a long time, early comments include Mandelbrot (1963) and Officer (1973). It was also clear to the founding fathers of modern continuous time finance that homogeneity was an unrealistic if convenient simplification, e.g. Black and Scholes (1972, p. 416) wrote “... there is evidence of nonstationarity in the variance. More work must be done to predict variances using the information available. ” Heterogeneity has deep implications for the theory and practice of financial economics and econometrics. In particular, asset pricing theory is dominated by the idea that higher rewards may be expected when we face higher risks, but these risks change through time in complicated ways. Some of the changes in the level of risk can be modelled stochastically, where the level of volatility and degree of codependence between assets is allowed to change over time. Such models allow us to explain, for example, empirically observed departures from BlackScholesMerton prices for options and understand why we should expect to see occasional dramatic moves in financial markets. The outline of this article is as follows. In section 2 I will trace the origins of SV and provide links with the basic models used today in the literature. In section 3 I will briefly discuss some of the innovations in the second generation of SV models. In section 4 I will briefly discuss the literature on conducting inference for SV models. In section 5 I will talk about the use of SV to price options. In section 6 I will consider the connection of SV with realised volatility. A extensive reviews of this literature is given in Shephard (2005). 2 The origin of SV models The origins of SV are messy, I will give five accounts, which attribute the subject to different sets of people.
2006), The role of implied volatility in forecasting future realized volatility and jumps in foreign exchange, stock, and bond markets
"... We study the forecasting of future realized volatility in the foreign exchange, stock, and bond markets from variables in the information set, including implied volatility backed out from option prices. Realized volatility is separated into its continuous and jump components, and the heterogeneous a ..."
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Cited by 20 (0 self)
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We study the forecasting of future realized volatility in the foreign exchange, stock, and bond markets from variables in the information set, including implied volatility backed out from option prices. Realized volatility is separated into its continuous and jump components, and the heterogeneous autoregressive (HAR) model is applied with implied volatility as an additional forecasting variable. A vector HAR (VecHAR) model for the resulting simultaneous system is introduced, controlling for possible endogeneity issues. We
nd that implied volatility contains incremental information about future volatility in all three markets, relative to past continuous and jump components, and it is an unbiased forecast in the foreign exchange and stock markets. Outofsample forecasting experiments con
rm that implied volatility is important in forecasting future realized volatility components in all three markets. Perhaps surprisingly, the jump component is, to some extent, predictable, and options appear calibrated to incorporate information about future jumps in all three markets.
Power variation for Gaussian processes with stationary increments
"... We develop the asymptotic theory for the realised power variation of the processes X = φ • G, where G is a Gaussian process with stationary increments. More specifically, under some mild assumptions on the variance function of the increments of G and certain regularity condition on the path of the p ..."
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Cited by 16 (7 self)
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We develop the asymptotic theory for the realised power variation of the processes X = φ • G, where G is a Gaussian process with stationary increments. More specifically, under some mild assumptions on the variance function of the increments of G and certain regularity condition on the path of the process φ we prove the convergence in probability for the properly normalised realised power variation. Moreover, under a further assumption on the Hölder index of the path of φ, we show an associated stable central limit theorem. The main tool is a general central limit theorem, due essentially to Hu & Nualart (2005), Nualart & Peccati (2005) and Peccati & Tudor (2005), for sequences of random variables which admit a chaos representation.
On the correlation structure of microstructure noise: A financial economic approach.
, 2010
"... We introduce the financial economics of market microstructure to the financial econometrics of asset return volatility estimation. In particular, we derive the crosscorrelation function between latent returns and market microstructure noise in several leading microstructure environments. We propose ..."
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Cited by 13 (2 self)
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We introduce the financial economics of market microstructure to the financial econometrics of asset return volatility estimation. In particular, we derive the crosscorrelation function between latent returns and market microstructure noise in several leading microstructure environments. We propose and illustrate several corresponding theoryinspired volatility estimators, which we apply to stock and oil prices. Our analysis and results are useful for assessing the validity of the frequentlyassumed independence of latent price and microstructure noise, for explaining observed crosscorrelation patterns, for predicting asyet undiscovered patterns, and most importantly, for promoting improved microstructurebased volatility empirics and improved empirical microstructure studies. Simultaneously and conversely, our analysis is far from the last word on the subject, as it is based on stylized benchmark models; it comes with a "call to action" for development and use of richer microstructure models in volatility estimation and beyond.
Bipower variation for Gaussian processes with stationary increments
"... Convergence in probability and central limit laws of bipower variation for Gaussian processes with stationary increments and for integrals with respect to such processes are derived. The main tools of the proofs are some recent powerful techniques of Wiener/Itô/Malliavin calculus for establishing li ..."
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Cited by 12 (1 self)
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Convergence in probability and central limit laws of bipower variation for Gaussian processes with stationary increments and for integrals with respect to such processes are derived. The main tools of the proofs are some recent powerful techniques of Wiener/Itô/Malliavin calculus for establishing limit laws, due to Nualart, Peccati and others.