Microstructure Noise in the Continuous Case: The Pre-Averaging Approach ∗
TL;DR: In this article, a generalized pre-averaging approach for estimating the integrated volatility is presented, which can generate rate optimal estimators with convergence rate n 1/4. But the convergence rate is not guaranteed.
About: This article is published in Stochastic Processes and their Applications.The article was published on 2009-07-01 and is currently open access. It has received 525 citations till now. The article focuses on the topics: Stochastic volatility & Estimator.
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TL;DR: In this article, realised kernels are used to carry out efficient feasible inference on the expost variation of underlying equity prices in the presence of simple models of market frictions, where the weights can be chosen to achieve the best possible rate of convergence and to have an asymptotic variance which is close to that of the maximum likelihood estimator in the parametric version of this problem.
Abstract: This paper shows how to use realised kernels to carry out efficient feasible inference on the expost variation of underlying equity prices in the presence of simple models of market frictions. The issue is subtle with only estimators which have symmetric weights delivering consistent estimators with mixed Gaussian limit theorems. The weights can be chosen to achieve the best possible rate of convergence and to have an asymptotic variance which is close to that of the maximum likelihood estimator in the parametric version of this problem. Realised kernels can also be selected to (i) be analysed using endogenously spaced data such as that in databases on transactions, (ii) allow for market frictions which are endogenous, (iii) allow for temporally dependent noise. The finite sample performance of our estimators is studied using simulation, while empirical work illustrates their use in practice.
1,269 citations
TL;DR: In this article, the authors compare the estimates based on trade and quote data for the same stock and find a remarkable level of agreement, which is due to non-trivial liquidity effects.
Abstract: Realised kernels use high frequency data to estimate daily volatility of individual stock prices. They can be applied to either trade or quote data. Here we provide the details of how we suggest implementing them in practice. We compare the estimates based on trade and quote data for the same stock and find a remarkable level of agreement. We identify some features of the high frequency data which are challenging for realised kernels. They are when there are local trends in the data, over periods of around 10 minutes, where the prices and quotes are driven up or down. These can be associated with high volumes. One explanation for this is that they are due to non-trivial liquidity effects.
543 citations
TL;DR: In this paper, the authors compare the estimates based on trade and quote data for the same stock and find a remarkable level of agreement, which is due to non-trivial liquidity effects.
Abstract: Summary Realized kernels use high-frequency data to estimate daily volatility of individual stock prices. They can be applied to either trade or quote data. Here we provide the details of how we suggest implementing them in practice. We compare the estimates based on trade and quote data for the same stock and find a remarkable level of agreement.
We identify some features of the high-frequency data, which are challenging for realized kernels. They are when there are local trends in the data, over periods of around 10 minutes, where the prices and quotes are driven up or down. These can be associated with high volumes. One explanation for this is that they are due to non-trivial liquidity effects.
459 citations
TL;DR: In this article, a multivariate realised kernel is proposed to estimate the ex-post covariation of log-prices, which is guaranteed to be positive semi-definite and robust to measurement noise of certain types.
441 citations
TL;DR: In this paper, a class of high-frequency-based volatility (HEAVY) models are presented, which are direct models of daily asset return volatility based on realised measures constructed from highfrequency data.
Abstract: This paper studies in some detail a class of high-frequency-based volatility (HEAVY) models These models are direct models of daily asset return volatility based on realised measures constructed from high-frequency data Our analysis identifies that the models have momentum and mean reversion effects, and that they adjust quickly to structural breaks in the level of the volatility process We study how to estimate the models and how they perform through the credit crunch, comparing their fit to more traditional GARCH models We analyse a model-based bootstrap which allows us to estimate the entire predictive distribution of returns We also provide an analysis of missing data in the context of these models Copyright © 2010 John Wiley & Sons, Ltd
431 citations
References
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TL;DR: In this paper, a closed-form solution for the price of a European call option on an asset with stochastic volatility is derived based on characteristi c functions and can be applied to other problems.
Abstract: I use a new technique to derive a closed-form solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond options and foreign currency options. Simulations show that correlation between volatility and the spot asset’s price is important for explaining return skewness and strike-price biases in the BlackScholes (1973) model. The solution technique is based on characteristi c functions and can be applied to other problems.
7,867 citations
Book•
01 Jan 1987
TL;DR: In this article, the General Theory of Stochastic Processes, Semimartingales, and Stochastically Integrals is discussed and the convergence of Processes with Independent Increments is discussed.
Abstract: I. The General Theory of Stochastic Processes, Semimartingales and Stochastic Integrals.- II. Characteristics of Semimartingales and Processes with Independent Increments.- III. Martingale Problems and Changes of Measures.- IV. Hellinger Processes, Absolute Continuity and Singularity of Measures.- V. Contiguity, Entire Separation, Convergence in Variation.- VI. Skorokhod Topology and Convergence of Processes.- VII. Convergence of Processes with Independent Increments.- VIII. Convergence to a Process with Independent Increments.- IX. Convergence to a Semimartingale.- X. Limit Theorems, Density Processes and Contiguity.- Bibliographical Comments.- References.- Index of Symbols.- Index of Terminology.- Index of Topics.- Index of Conditions for Limit Theorems.
5,987 citations
TL;DR: In this article, a voluminous literature has emerged for modeling the temporal dependencies in financial market volatility using ARCH and stochastic volatility models and it has been shown that volatility models produce strikingly accurate inter-daily forecasts for the latent volatility factor that would be of interest in most financial applications.
Abstract: A voluminous literature has emerged for modeling the temporal dependencies in financial market volatility using ARCH and stochastic volatility models. While most of these studies have documented highly significant in-sample parameter estimates and pronounced intertemporal volatility persistence, traditional ex-post forecast evaluation criteria suggest that the models provide seemingly poor volatility forecasts. Contrary to this contention, we show that volatility models produce strikingly accurate interdaily forecasts for the latent volatility factor that would be of interest in most financial applications. New methods for improved ex-post interdaily volatility measurements based on high-frequency intradaily data are also discussed.
3,174 citations
TL;DR: In this article, the authors provide a general framework for integration of high-frequency intraday data into the measurement, modeling, and forecasting of daily and lower frequency volatility and return distributions.
Abstract: This paper provides a general framework for integration of high-frequency intraday data into the measurement, modeling, and forecasting of daily and lower frequency volatility and return distributions. Most procedures for modeling and forecasting financial asset return volatilities, correlations, and distributions rely on restrictive and complicated parametric multivariate ARCH or stochastic volatility models, which often perform poorly at intraday frequencies. Use of realized volatility constructed from high-frequency intraday returns, in contrast, permits the use of traditional time series procedures for modeling and forecasting. Building on the theory of continuous-time arbitrage-free price processes and the theory of quadratic variation, we formally develop the links between the conditional covariance matrix and the concept of realized volatility. Next, using continuously recorded observations for the Deutschemark / Dollar and Yen / Dollar spot exchange rates covering more than a decade, we find that forecasts from a simple long-memory Gaussian vector autoregression for the logarithmic daily realized volatilities perform admirably compared to popular daily ARCH and related models. Moreover, the vector autoregressive volatility forecast, coupled with a parametric lognormal-normal mixture distribution implied by the theoretically and empirically grounded assumption of normally distributed standardized returns, gives rise to well-calibrated density forecasts of future returns, and correspondingly accurate quantile estimates. Our results hold promise for practical modeling and forecasting of the large covariance matrices relevant in asset pricing, asset allocation and financial risk management applications.
2,823 citations
TL;DR: In this article, the effective bid-ask spread is measured by Spread = 2−cov where cov is the first-order serial covariance of price changes, and is shown empirically to be closely related to firm size.
Abstract: In an efficient market, the fundamental value of a security fluctuates randomly. However, trading costs induce negative serial dependence in successive observed market price changes. In fact, given market efficiency, the effective bid-ask spread can be measured by Spread=2−cov where “cov” is the first-order serial covariance of price changes. This implicit measure of the bid-ask spread is derived formally and is shown empirically to be closely related to firm size.
2,781 citations