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Author: Robert Ślepaczuk
Publisher: LAP Lambert Academic Publishing
ISBN: 9783844356939
Category :
Languages : en
Pages : 60
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Book Description
This paper focuses on volatility of financial markets, which is one of the most important issues in finance, especially with regards to modelling high-frequency data. Risk management, asset pricing and option valuation techniques are the areas where the concept of volatility estimators (consistent, unbiased and the most efficient) is of crucial concern. Our intention was to find the best estimator of true volatility taking into account the latest investigations in finance literature. Basing on the methodology presented in previous papers on volatility estimators, we computed the various model-free volatility estimators and compared them with classical volatility estimator. In order to reveal the information set hidden in high-frequency data, we utilized the concept of realized volatility and realized range. Calculating our estimator, we carefully focused on (the interval used in calculation), n (the memory of the process) and q (scaling factor). Our results revealed that the appropriate selection of and n plays the crucial role in estimator efficiency, as well as its accuracy...This work was supported by the Foundation for Polish Science."
Author: Robert Ślepaczuk
Publisher: LAP Lambert Academic Publishing
ISBN: 9783844356939
Category :
Languages : en
Pages : 60
Get Book Here
Book Description
This paper focuses on volatility of financial markets, which is one of the most important issues in finance, especially with regards to modelling high-frequency data. Risk management, asset pricing and option valuation techniques are the areas where the concept of volatility estimators (consistent, unbiased and the most efficient) is of crucial concern. Our intention was to find the best estimator of true volatility taking into account the latest investigations in finance literature. Basing on the methodology presented in previous papers on volatility estimators, we computed the various model-free volatility estimators and compared them with classical volatility estimator. In order to reveal the information set hidden in high-frequency data, we utilized the concept of realized volatility and realized range. Calculating our estimator, we carefully focused on (the interval used in calculation), n (the memory of the process) and q (scaling factor). Our results revealed that the appropriate selection of and n plays the crucial role in estimator efficiency, as well as its accuracy...This work was supported by the Foundation for Polish Science."
Author: Gilles O. Zumbach
Publisher:
ISBN:
Category :
Languages : en
Pages : 22
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Book Description
The limitations of volatilities computed with daily data as well as simple statistical considerations strongly suggest to use intraday data in order to obtain accurate volatility estimates. Under a continuous time arbitrage-free setup, the quadratic variations of the prices would allow us, in principle, to construct an approximately error free estimate of volatility by using data at the highest frequency available. Yet, empirical data at very short time scales differ in many ways from the arbitrage-free continuous time price processes. For foreign exchange rates, the main difference originates in the incoherent structure of the price formation process. This market micro-structure effect introduces a noisy component in the price process leading to a strong overestimation of volatility when using naive estimators. Therefore, to be able to fully exploit the information contained in high frequency data, this incoherent effect needs to be discounted. In this contribution, we investigate several unbiased estimators that take into account the incoherent noise. One approach is to use a filter for pre-whitening the prices, and then using volatility estimators based on the filtered series. Another solution is to directly define a volatility estimator using tick-by-tick price differences, and including a correction term for the price formation effect. The properties of these estimators are investigated by Monte Carlo simulations. A number of important real-world effects are included in the simulated processes: realistic volatility and price dynamic, the incoherent effect, seasonalities, and random arrival time of ticks. Moreover, we investigate the robustness of the estimators with respect to data frequency changes and gaps. Finally, we illustrate the behavior of the best estimators on empirical data.
Author: Simona Sanfelici
Publisher:
ISBN:
Category :
Languages : en
Pages : 30
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Book Description
We define a new consistent estimator of the integrated volatility of volatility based only on a pre-estimation of the Fourier coefficients of the volatility process. We investigate the finite sample properties of the estimator in the presence of noise contamination by computing the bias of the estimator due to noise and showing that it vanishes as the number of observations increases, under suitable assumptions. In both simulated and empirical studies, the performance of the Fourier estimator with high frequency data is investigated and it is shown that the proposed estimator of volatility of volatility is easily implementable, computationally stable and even robust to market microstructure noise.
Author: Xinyu Song
Publisher:
ISBN:
Category :
Languages : en
Pages : 68
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Book Description
In this dissertation, we present the topic on volatility analysis with combined discrete-time and continuous-time models by employing low-frequency, high-frequency and option data. We first investigate the traditional low-frequency approach for volatility analysis that frequently adopts generalized autoregressive conditional heteroscedastic (GARCH) type models and modern high-frequency approach for volatility estimation that often employs realized volatility type estimators, examples include multi-scale realized volatility estimators, pre-averaging realized volatility estimators and kernel realized volatility estimators. We introduce a new model for volatility analysis by combining low-frequency and high-frequency approaches. The proposed model is an Ito diffusion process where the instantaneous volatility depends on integrated volatility and squared log return. When the model is restricted to integer times, conditional volatility of the process adopts an analogous structure with the one seen in a standard GARCH model and includes one additional innovation: the integrated volatility. The proposed model is named as generalized unified GARCH-Ito model. Parameter estimation is built on the marriage of a quasi-likelihood function obtained based on conditional volatility structure from the proposed model and common realized volatility estimators obtained based on high-frequency financial data. To improve the performance of proposed estimators, we also provide the option of incorporating option data by adopting a joint quasi-likelihood function. We study the asymptotic behaviors of proposed estimators and conduct a simulation study that confirms proposed estimators have good finite sample statistical performance. An empirical study has been carried out to demonstrate the ease of implementation of the proposed model in daily volatility estimation.
Author: Yacine Ait-Sahalia
Publisher:
ISBN:
Category :
Languages : en
Pages : 43
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Book Description
We analyze the impact of time series dependence in market microstructure noise on the properties of estimators of the integrated volatility of an asset price based on data sampled at frequencies high enough for that noise to be a dominant consideration. We show that combining two time scales for that purpose will work even when the noise exhibits time series dependence, analyze in that context a refinement of this approach based on multiple time scales, and compare empirically our different estimators to the standard realized volatility.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Frederi G. Viens
Publisher: John Wiley & Sons
ISBN: 0470876883
Category : Business & Economics
Languages : en
Pages : 468
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Book Description
CUTTING-EDGE DEVELOPMENTS IN HIGH-FREQUENCY FINANCIAL ECONOMETRICS In recent years, the availability of high-frequency data and advances in computing have allowed financial practitioners to design systems that can handle and analyze this information. Handbook of Modeling High-Frequency Data in Finance addresses the many theoretical and practical questions raised by the nature and intrinsic properties of this data. A one-stop compilation of empirical and analytical research, this handbook explores data sampled with high-frequency finance in financial engineering, statistics, and the modern financial business arena. Every chapter uses real-world examples to present new, original, and relevant topics that relate to newly evolving discoveries in high-frequency finance, such as: Designing new methodology to discover elasticity and plasticity of price evolution Constructing microstructure simulation models Calculation of option prices in the presence of jumps and transaction costs Using boosting for financial analysis and trading The handbook motivates practitioners to apply high-frequency finance to real-world situations by including exclusive topics such as risk measurement and management, UHF data, microstructure, dynamic multi-period optimization, mortgage data models, hybrid Monte Carlo, retirement, trading systems and forecasting, pricing, and boosting. The diverse topics and viewpoints presented in each chapter ensure that readers are supplied with a wide treatment of practical methods. Handbook of Modeling High-Frequency Data in Finance is an essential reference for academics and practitioners in finance, business, and econometrics who work with high-frequency data in their everyday work. It also serves as a supplement for risk management and high-frequency finance courses at the upper-undergraduate and graduate levels.
Author: David Schreindorfer
Publisher:
ISBN:
Category : Analysis of variance
Languages : en
Pages : 164
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Book Description
Author: Maria Elvira Mancino
Publisher: Springer
ISBN: 3319509691
Category : Mathematics
Languages : en
Pages : 139
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Book Description
This volume is a user-friendly presentation of the main theoretical properties of the Fourier-Malliavin volatility estimation, allowing the readers to experience the potential of the approach and its application in various financial settings. Readers are given examples and instruments to implement this methodology in various financial settings and applications of real-life data. A detailed bibliographic reference is included to permit an in-depth study.
Author: Xin Zhang
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
This dissertation work focuses on developing statistical methods for volatility estimation and prediction with high frequency financial data. We consider two kinds of volatility: integrated volatility and jump variation. In the first part, we introduce the methods for integrated volatility estimation with the presence of microstructure noise. We will first talk about the optimal sampling frequency for integrated volatility estimation since subsampling is very popular in practice. Then we will discuss about those methods based on subsampling. Two-scale estimator is developed using the subsampling idea while taking advantage of all of the data. An extension to the multi-scale further improves the efficiency of the estimation. In the second part, we propose a heterogenous autoregressive model for the integrated volatility estimators based on subsampling. An empirical approach is to estimate integrated volatility using high frequency data and then fit the estimates to a low frequency heterogeneous autoregressive volatility model for prediction. We provide some theoretical justifications for the empirical approach by showing that these estimators approximately obey a heterogenous autoregressive model for some appropriate underlying price and volatility processes. In the third part, we propose a method for jump variation estimation using wavelet techniques. Previously, jumps are not assumed in the model. In this part, we will concentrate on jump variation estimation and there- fore, we will be able to estimate the integrated volatility and jump variation individually. We show that by choosing a threshold, we will be able to detect the jump location, and by using the realized volatility processes instead of the original price process, we will be able to improve the convergence rate of estimation. We include both numerical and empirical results of this method.
