Essays on Estimation and Inference for Volatility with High Frequency Data PDF Download

Author: Ilze Kalnina
Publisher:
ISBN:
Category : Academic theses
Languages : en
Pages : 0

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Author: Yucheng Sun
Publisher:
ISBN:
Category :
Languages : en
Pages : 125

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Based on high-frequency price data, this thesis focuses on estimating the realized covariance and the integrated volatility of asset prices, and applying volatility estimation to price jump detection. The first chapter uses the LASSO procedure to regularize some estimators of high dimensional realized covariance matrices. We establish theoretical properties of the regularized estimators that show its estimation precision and the probability that they correctly reveal the network structure of the assets. The second chapter proposes a novel estimator of the integrated volatility which is the quadratic variation of the continuous part in the price process. This estimator is obtained by truncating the two-scales realized variance estimator. We show its consistency in the presence of market microstructure noise and finite or infinite activity jumps in the price process. The third chapter employs this estimator to design a test to explore the existence of price jumps with noisy price data.

Author: Md. Nazmul Ahsan
Publisher:
ISBN:
Category :
Languages : en
Pages :

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"Although stochastic volatility (SV) models have many appealing features, estimation and inference on SV models are challenging problems due to the inherent difficulty of evaluating the likelihood function. The existing methods are either computationally costly and/or inefficient. This thesis studies and contributes to the SV literature from the estimation, inference, and volatility forecasting viewpoints. It consists of three essays, which include both theoretical and empirical contributions. On the whole, the thesis develops easily applicable statistical methods for stochastic volatility models.The first essay proposes computationally simple moment-based estimators for the first-order SV model. In addition to confirming the enormous computational advantage of the proposed estimators, the results show that the proposed estimators match (or exceed) alternative estimators in terms of precision – including Bayesian estimators proposed in this context, which have the best performance among alternative estimators. Using this simple estimator, we study three crucial test problems (no persistence, no latent specification of volatility, and no stochastic volatility hypothesis), and evaluate these null hypotheses in three ways: asymptotic critical values, a parametric bootstrap procedure, and a maximized Monte Carlo procedure. The proposed methods are applied to daily observations on the returns for three major stock prices [Coca-Cola, Walmart, Ford], and the Standard and Poor’s Composite Price Index. The results show the presence of stochastic volatility with strong persistence.The second essay studies the problem of estimating higher-order stochastic volatility [SV(p)] models. The estimation of SV(p) models is even more challenging and rarely considered in the literature. We propose several estimators for higher-order stochastic volatility models. Among these, the simple winsorized ARMA-based estimator is uniformly superior in terms of bias and RMSE to other estimators, including the Bayesian MCMC estimator. The proposed estimators are applied to stock return data, and the usefulness of the proposed estimators is assessed in two ways. First, using daily returns on the S&P 500 index from 1928 to 2016, we find that higher-order SV models – in particular an SV(3) model – are preferable to an SV(1), from the viewpoints of model fit and both asymptotic and finite-sample tests. Second, using different volatility proxies (squared return and realized volatility), we find that higher-order SV models are preferable for out-of-sample volatility forecasting, whether a high volatility period (such as financial crisis) is included in the estimation sample or the forecasted sample. Our results highlight the usefulness of higher-order SV models for volatility forecasting.In the final essay, we introduce a novel class of generalized stochastic volatility (GSV) models which utilize high-frequency (HF) information (realized volatility (RV) measures). GSV models can accommodate nonstationary volatility process, various distributional assumptions, and exogenous regressors in the latent volatility equation. Instrumental variable methods are employed to provide a unified framework for the analysis (estimation and inference) of GSV models. We consider the parameter inference problem in GSV models with nonstationary volatility and develop identification-robust methods for joint hypotheses involving the volatility persistence parameter and the autocorrelation parameter of the composite error (or the noise ratio). For distributional theory, three different sets of assumptions are considered. In simulations, the proposed tests outperform the usual asymptotic test regarding size and exhibit excellent power. We apply our inference methods to IBM price and option data andidentify several empirical relationships"--

Author: Jonathan H. Wright
Publisher:
ISBN:
Category : Rate of return
Languages : en
Pages : 38

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While it is clear that the volatility of asset returns is serially correlated, there is no general agreement as to the most appropriate parametric model for characterizing this temporal dependence. In this paper, we propose a simple way of modeling financial market volatility using high frequency data. The method avoids using a tight parametric model, by instead simply fitting a long autoregression to log-squared, squared or absolute high frequency returns. This can either be estimated by the usual time domain method, or alternatively the autoregressive coefficients can be backed out from the smoothed periodogram estimate of the spectrum of log-squared, squared or absolute returns. We show how this approach can be used to construct volatility forecasts, which compare favorably with some leading alternatives in an out-of-sample forecasting exercise.

Author: Ji Shen
Publisher:
ISBN:
Category :
Languages : en
Pages : 105

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Author: Haiqing Zheng
Publisher:
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Category :
Languages : en
Pages : 134

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Author: Sebastian Trojan
Publisher:
ISBN:
Category :
Languages : en
Pages : 199

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The first essay describes a very general stochastic volatility (SV) model specification with leverage, heavy tails, skew and switching regimes, using realized volatility (RV) as an auxiliary time series to improve inference on latent volatility. The information content of the range and of implied volatility using the VIX index is also analyzed. Database is the S&P 500 index. Asymmetry in the observation error is modeled by the generalized hyperbolic skew Student-t distribution, whose heavy and light tail enable substantial skewness. Resulting number of regimes and dynamics differ dependent on the auxiliary volatility proxy and are investigated in-sample for the financial crash period 2008/09 in more detail. An out-of-sample study comparing predictive ability of various model variants for a calm and a volatile period yields insights about the gains on forecasting performance from different volatility proxies. Results indicate that including RV or the VIX pays off mostly in more volatile market conditions, whereas in calmer environments SV specifications using no auxiliary series outperform. The range as volatility proxy provides a superior in-sample fit, but its predictive performance is found to be weak. The second essay presents a high frequency stochastic volatility model. Price duration and associated absolute price change in event time are modeled contemporaneously to fully capture volatility on the tick level, combining the SV and stochastic conditional duration (SCD) model. Estimation is with IBM stock intraday data 2001/10 (decimalization completed), taking a minimum midprice threshold of a half tick. Persistent information flow is extracted, featuring a positively correlated innovation term and negative cross effects in the AR(1) persistence matrix. Additionally, regime switching in both duration and absolute price change is introduced to increase nonlinear capabilities of the model. Thereby, a separate price jump.

Author: Yacine Aït-Sahalia
Publisher: Princeton University Press
ISBN: 0691161437
Category : Business & Economics
Languages : en
Pages : 683

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A comprehensive introduction to the statistical and econometric methods for analyzing high-frequency financial data High-frequency trading is an algorithm-based computerized trading practice that allows firms to trade stocks in milliseconds. Over the last fifteen years, the use of statistical and econometric methods for analyzing high-frequency financial data has grown exponentially. This growth has been driven by the increasing availability of such data, the technological advancements that make high-frequency trading strategies possible, and the need of practitioners to analyze these data. This comprehensive book introduces readers to these emerging methods and tools of analysis. Yacine Aït-Sahalia and Jean Jacod cover the mathematical foundations of stochastic processes, describe the primary characteristics of high-frequency financial data, and present the asymptotic concepts that their analysis relies on. Aït-Sahalia and Jacod also deal with estimation of the volatility portion of the model, including methods that are robust to market microstructure noise, and address estimation and testing questions involving the jump part of the model. As they demonstrate, the practical importance and relevance of jumps in financial data are universally recognized, but only recently have econometric methods become available to rigorously analyze jump processes. Aït-Sahalia and Jacod approach high-frequency econometrics with a distinct focus on the financial side of matters while maintaining technical rigor, which makes this book invaluable to researchers and practitioners alike.

Author: Ying Gu
Publisher:
ISBN:
Category : Derivative securities
Languages : en
Pages : 155

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Author:
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ISBN:
Category :
Languages : en
Pages : 0

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Modeling and estimating volatility plays a crucial role in financial practice. Devoted efforts are made to investigate this topic using both low-frequency and high-frequency financial data. Traditionally, volatility modeling and analysis are based on either historical price data or option data. Finance theory shows that option prices heavily depend on the underlying stocks' prices, and thus the two kinds of data are related. This thesis explores the approach that combines both stock price data and option data to perform the statistical analysis of volatility. We investigate the Black-Scholes model and an exponential GARCH model and derive the relationship among the Fisher information for volatility estimation based on stock price data alone or option data alone as well as joint volatility estimation for combining stock price data and option data. Under the Block-Scholes model, asymptotic theory for the joint estimation is established, and a simulation study was conducted to check finite sample performances of the proposed joint estimator. Being more accessible than ever, high-frequency data have provided researchers and practitioners with incredible tools to investigate assets pricing and market dynamics. Non-synchronous observations, microstructure noise, and complex pricing models are challenges coming along with high-frequency data. Moreover, large volatility matrix estimation is involved in many finance practices and encounters "curse of dimensionality". Although it is widely used in large covariance estimation, imposing sparsity assumption on the entire volatility matrix is not reasonable in financial practice. In fact, due to the existence of common factors, assets are widely correlated with each other and their volatility matrix is not sparse. In this thesis, we focus on incorporating the factor influence in asset price modeling and volatility matrix estimation. We propose to model asset price using a factor-based diffusion process. The idea is that assets' prices are governed by a common factor, and that assets with similar characteristics share the same association with the factor. Under the proposed factor-based model, we developed an estimation scheme called "Blocking and Regularizing", which deals with all of the four changeless. The asymptotic properties of the proposed estimator are studied, while its finite sample performance is tested via extensive numerical studies to support theoretical results