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Discrete Time Series, Processes, and Applications in Finance / by Gilles Zumbach
Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Reihen: Springer Finance | SpringerLink BücherVerlag: Berlin ; Heidelberg : Springer, 2013Beschreibung: Online-Ressource (XXI, 317 p. 103 illus., 101 illus. in color, digital)ISBN:- 9783642317422
- Finanzmarkt
- Zeitreihenanalyse
- Finanzmathematik
- ARCH-Modell
- Stochastischer Prozess
- Volatilität
- Risikomaß
- Optionspreistheorie
- Theorie
- Kreditmarkt
- Portfolio Selection
- Risikomanagement
- Economics
- Mathematics
- Finance
- Distribution (Probability theory)
- Economics, Mathematical
- Probabilities
- Statistics
- Social sciences
- 519
- HB135-147
Inhalte:
Zusammenfassung: Preface -- List of Figures.-List of Tables -- 1. Introduction -- 2.Notation, naming and general definitions -- 3.Stylized facts -- 4.Empirical mug shots -- 5.Process Overview -- 6.Logarithmic versus relative random walks -- 7.ARCH processes -- 8.Stochastic volatility processes -- 9.Regime switching process -- 10.Price and volatility using high-frequency data -- 11.Time reversal asymmetry -- 12.Characterizing heteroskedasticity -- 13.The innovation distributions -- 14.Leverage effect -- 15.Processes and market risk evaluation -- 16.Option pricing -- 17.Properties of large covariance matrices -- 18.Multivariate ARCH processes -- 19.The processes compatible with the stylized facts -- 20.Further thoughts.-Bibliography -- Index.Zusammenfassung: Most financial and investment decisions are based on considerations of possible future changes and require forecasts on the evolution of the financial world. Time series and processes are the natural tools for describing the dynamic behavior of financial data, leading to the required forecasts. This book presents a survey of the empirical properties of financial time series, their descriptions by means of mathematical processes, and some implications for important financial applications used in many areas like risk evaluation, option pricing or portfolio construction. The statistical tools used to extract information from raw data are introduced. Extensive multiscale empirical statistics provide a solid benchmark of stylized facts (heteroskedasticity, long memory, fat-tails, leverage…), in order to assess various mathematical structures that can capture the observed regularities. The author introduces a broad range of processes and evaluates them systematically against the benchmark, summarizing the successes and limitations of these models from an empirical point of view. The outcome is that only multiscale ARCH processes with long memory, discrete multiplicative structures and non-normal innovations are able to capture correctly the empirical properties. In particular, only a discrete time series framework allows to capture all the stylized facts in a process, whereas the stochastic calculus used in the continuum limit is too constraining. The present volume offers various applications and extensions for this class of processes including high-frequency volatility estimators, market risk evaluation, covariance estimation and multivariate extensions of the processes. The book discusses many practical implications and is addressed to practitioners and quants in the financial industry, as well as to academics, including graduate (Master or PhD level) students. The prerequisites are basic statistics and some elementary financial mathematics. Gilles Zumbach has worked for several institutions, including banks, hedge funds and service providers and continues to be engaged in research on many topics in finance. His primary areas of interest are volatility, ARCH processes and financial applications.PPN: PPN: 1651886148Package identifier: Produktsigel: ZDB-2-SXMS | ZDB-2-SMA | ZDB-2-SEB
Discrete Time Series, Processes, and Applications in Finance; Contents; List of Figures; List of Tables; Chapter 1: Introduction; Chapter 2: Notation, Naming, and General Definitions; 2.1 Time, Time Interval, and Time Scale; 2.2 Time Series; 2.2.1 Historical, Centered and Realized Quantities; 2.2.2 Returns; 2.2.3 Volatilities; 2.2.4 Volatility Increments; 2.3 Average, Expectation; 2.4 Scaling, Annualization, and Reference Time Interval; 2.5 EMA, MA, and Operators on Time Series; 2.6 Computation of the Histograms and Pdf; Chapter 3: Stylized Facts; 3.1 Introduction
3.2 Probability Density Function3.2.1 Pdf for the Return; 3.2.2 Pdf for the Volatility; 3.2.3 Pdf for the Volatility Increment; 3.3 Scaling for the Moments: The Width of the Pdf; 3.3.1 Introduction; 3.3.2 Scaling for the Return; 3.3.3 Scaling for the Volatility; 3.4 Relative Excess Kurtosis: The Shape of the Pdf; 3.4.1 Introduction; 3.4.2 Relative Excess Kurtosis for the Return; 3.4.3 Relative Excess Kurtosis for the Volatility; 3.4.4 Relative Excess Kurtosis for the Volatility Increment; 3.5 Lagged Correlations; 3.5.1 Introduction; 3.5.2 Lagged Correlations for the Absolute Return
3.5.3 Lagged Correlations for the Volatility3.6 Correlation with the Realized Volatility; 3.6.1 Introduction; 3.6.2 Autocorrelation for the Volatility; 3.6.3 Correlations Between the Historical and Realized Volatilities; 3.6.4 Correlations Between the Realized Volatility and the Historical Volatility Increment; 3.6.5 Correlations of the Realized Volatilities with the Centered Volatility Increment; 3.7 Correlation for the Volatility Increment; 3.8 Volatility Graining; 3.9 Trend and Leverage Effects; 3.9.1 Historical Return Versus Realized Volatility Correlation
3.9.2 Trend/Drift Versus Realized Volatility Correlation3.10 Time Reversal Invariance; Chapter 4: Empirical Mug Shots; Chapter 5: Process Overview; 5.1 Why Using a Finite Time Increment for the Processes?; 5.2 The Definition of the Returns; 5.3 The Most Important Stylized Facts; 5.4 ARCH Processes; 5.5 Stochastic Volatility Processes; 5.6 Regime-Switching Processes; 5.7 The Plan for the Forthcoming Chapters; Chapter 6: Logarithmic Versus Relative Random Walks; 6.1 Motivations; 6.2 The Definitions of the Return; 6.3 Logarithmic Process: One Asset, Constant Volatility
6.4 Geometric Process: One Asset, Constant Volatility6.5 Long Time Properties of the (Constant Volatility) Random Walk Process; 6.6 Geometric Process: Many Assets, Constant Volatility; 6.6.1 One Time-Step; 6.6.2 Many Time Steps; 6.7 Enforcing the Condition rrel> -1 or rrel>=-1; 6.8 Skewness; 6.9 The Broader Perspective So Far …; Chapter 7: ARCH Processes; 7.1 GARCH(1,1); 7.1.1 Volatility Forecast for the GARCH(1,1) Process*; 7.1.2 Computation for the Lagged Correlation*; 7.2 I-GARCH(2); 7.3 EGARCH(1,1); 7.4 Linear Versus Affine Processes; 7.5 Multicomponent ARCH Processes
7.6 General Considerations on Volatility Forecast
Preface -- List of Figures.-List of Tables -- 1. Introduction -- 2.Notation, naming and general definitions -- 3.Stylized facts -- 4.Empirical mug shots -- 5.Process Overview -- 6.Logarithmic versus relative random walks -- 7.ARCH processes -- 8.Stochastic volatility processes -- 9.Regime switching process -- 10.Price and volatility using high-frequency data -- 11.Time reversal asymmetry -- 12.Characterizing heteroskedasticity -- 13.The innovation distributions -- 14.Leverage effect -- 15.Processes and market risk evaluation -- 16.Option pricing -- 17.Properties of large covariance matrices -- 18.Multivariate ARCH processes -- 19.The processes compatible with the stylized facts -- 20.Further thoughts.-Bibliography -- Index..
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