Ebook: Discrete Time Series, Processes, and Applications in Finance

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.

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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.

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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.

Content:
Front Matter....Pages I-XXI
Introduction....Pages 1-5
Notation, Naming, and General Definitions....Pages 7-16
Stylized Facts....Pages 17-47
Empirical Mug Shots....Pages 49-55
Process Overview....Pages 57-67
Logarithmic Versus Relative Random Walks....Pages 69-84
ARCH Processes....Pages 85-128
Stochastic Volatility Processes....Pages 129-141
Regime-Switching Process....Pages 143-145
Price and Volatility Using High-Frequency Data....Pages 147-161
Time-Reversal Asymmetry....Pages 163-179
Characterizing Heteroscedasticity....Pages 181-196
The Innovation Distributions....Pages 197-203
Leverage Effect....Pages 205-209
Processes and Market Risk Evaluation....Pages 211-231
Option Pricing....Pages 233-255
The Empirical Properties of Large Covariance Matrices....Pages 257-272
Multivariate ARCH Processes....Pages 273-294
The Processes Compatible with the Stylized Facts....Pages 295-298
Further Thoughts....Pages 299-307
Back Matter....Pages 309-319

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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.

Content:
Front Matter....Pages I-XXI
Introduction....Pages 1-5
Notation, Naming, and General Definitions....Pages 7-16
Stylized Facts....Pages 17-47
Empirical Mug Shots....Pages 49-55
Process Overview....Pages 57-67
Logarithmic Versus Relative Random Walks....Pages 69-84
ARCH Processes....Pages 85-128
Stochastic Volatility Processes....Pages 129-141
Regime-Switching Process....Pages 143-145
Price and Volatility Using High-Frequency Data....Pages 147-161
Time-Reversal Asymmetry....Pages 163-179
Characterizing Heteroscedasticity....Pages 181-196
The Innovation Distributions....Pages 197-203
Leverage Effect....Pages 205-209
Processes and Market Risk Evaluation....Pages 211-231
Option Pricing....Pages 233-255
The Empirical Properties of Large Covariance Matrices....Pages 257-272
Multivariate ARCH Processes....Pages 273-294
The Processes Compatible with the Stylized Facts....Pages 295-298
Further Thoughts....Pages 299-307
Back Matter....Pages 309-319
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