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Nonparametric Finance

E-BookEPUB2 - DRM Adobe / EPUBE-Book
704 Seiten
Englisch
John Wiley & Sonserschienen am28.02.20181. Auflage
An Introduction to Machine Learning in Finance, With Mathematical Background, Data Visualization, and R

Nonparametric function estimation is an important part of machine learning, which is becoming increasingly important in quantitative finance. Nonparametric Finance provides graduate students and finance professionals with a foundation in nonparametric function

estimation and the underlying mathematics. Combining practical applications, mathematically rigorous presentation, and statistical data analysis into a single volume, this book presents detailed instruction in discrete chapters that allow readers to dip in as needed without reading from beginning to end.

Coverage includes statistical finance, risk management, portfolio management, and securities pricing to provide a practical knowledge base, and the introductory chapter introduces basic finance concepts for readers with a strictly mathematical background. Economic significance

is emphasized over statistical significance throughout, and R code is provided to help readers reproduce the research, computations, and figures being discussed. Strong graphical content clarifies the methods and demonstrates essential visualization techniques, while deep mathematical and statistical insight backs up practical applications.

Written for the leading edge of finance, Nonparametric Finance:

• Introduces basic statistical finance concepts, including univariate and multivariate data analysis, time series analysis, and prediction

• Provides risk management guidance through volatility prediction, quantiles, and value-at-risk

• Examines portfolio theory, performance measurement, Markowitz portfolios, dynamic portfolio selection, and more

• Discusses fundamental theorems of asset pricing, Black-Scholes pricing and hedging, quadratic pricing and hedging, option portfolios, interest rate derivatives, and other asset pricing principles

• Provides supplementary R code and numerous graphics to reinforce complex content

Nonparametric function estimation has received little attention in the context of risk management and option pricing, despite its useful applications and benefits. This book provides the essential background and practical knowledge needed to take full advantage of these little-used methods, and turn them into real-world advantage.

Jussi Klemelä, PhD, is Adjunct Professor at the University of Oulu. His research interests include nonparametric function estimation, density estimation, and data visualization. He is the author of Smoothing of Multivariate Data: Density Estimation and Visualization and Multivariate Nonparametric Regression and Visualization: With R and Applications to Finance.



Jussi Klemelä, PhD, is Adjunct Professor at the University of Oulu. His research interests include nonparametric function estimation, density estimation, and data visualization. He is the author of Smoothing of Multivariate Data: Density Estimation and Visualization and Multivariate Nonparametric Regression and Visualization: With R and Applications to Finance.mehr
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Produkt

KlappentextAn Introduction to Machine Learning in Finance, With Mathematical Background, Data Visualization, and R

Nonparametric function estimation is an important part of machine learning, which is becoming increasingly important in quantitative finance. Nonparametric Finance provides graduate students and finance professionals with a foundation in nonparametric function

estimation and the underlying mathematics. Combining practical applications, mathematically rigorous presentation, and statistical data analysis into a single volume, this book presents detailed instruction in discrete chapters that allow readers to dip in as needed without reading from beginning to end.

Coverage includes statistical finance, risk management, portfolio management, and securities pricing to provide a practical knowledge base, and the introductory chapter introduces basic finance concepts for readers with a strictly mathematical background. Economic significance

is emphasized over statistical significance throughout, and R code is provided to help readers reproduce the research, computations, and figures being discussed. Strong graphical content clarifies the methods and demonstrates essential visualization techniques, while deep mathematical and statistical insight backs up practical applications.

Written for the leading edge of finance, Nonparametric Finance:

• Introduces basic statistical finance concepts, including univariate and multivariate data analysis, time series analysis, and prediction

• Provides risk management guidance through volatility prediction, quantiles, and value-at-risk

• Examines portfolio theory, performance measurement, Markowitz portfolios, dynamic portfolio selection, and more

• Discusses fundamental theorems of asset pricing, Black-Scholes pricing and hedging, quadratic pricing and hedging, option portfolios, interest rate derivatives, and other asset pricing principles

• Provides supplementary R code and numerous graphics to reinforce complex content

Nonparametric function estimation has received little attention in the context of risk management and option pricing, despite its useful applications and benefits. This book provides the essential background and practical knowledge needed to take full advantage of these little-used methods, and turn them into real-world advantage.

Jussi Klemelä, PhD, is Adjunct Professor at the University of Oulu. His research interests include nonparametric function estimation, density estimation, and data visualization. He is the author of Smoothing of Multivariate Data: Density Estimation and Visualization and Multivariate Nonparametric Regression and Visualization: With R and Applications to Finance.



Jussi Klemelä, PhD, is Adjunct Professor at the University of Oulu. His research interests include nonparametric function estimation, density estimation, and data visualization. He is the author of Smoothing of Multivariate Data: Density Estimation and Visualization and Multivariate Nonparametric Regression and Visualization: With R and Applications to Finance.
Details
Weitere ISBN/GTIN9781119409120
ProduktartE-Book
EinbandartE-Book
FormatEPUB
Format Hinweis2 - DRM Adobe / EPUB
FormatFormat mit automatischem Seitenumbruch (reflowable)
Erscheinungsjahr2018
Erscheinungsdatum28.02.2018
Auflage1. Auflage
ReiheWiley Series in Probability and Statistics
Seiten704 Seiten
SpracheEnglisch
Dateigrösse49079 Kbytes
Artikel-Nr.3379473
Rubriken
Genre9201

Inhalt/Kritik

Leseprobe
Chapter 1
Introduction

Nonparametric function estimation has many useful applications in quantitative finance. We study four areas of quantitative finance: statistical finance, risk management, portfolio management, and pricing of securities.1

A main theme of the book is to study quantitative finance starting only with few modeling assumptions. For example, we study the performance of nonparametric prediction in portfolio selection, and we study the performance of nonparametric quadratic hedging in option pricing, without constructing detailed models for the markets. We use some classical parametric methods, such as Black-Scholes pricing, as benchmarks to provide comparisons with nonparametric methods.

A second theme of the book is to put emphasis on the study of economic significance instead of statistical significance. For example, studying economic significance in portfolio selection could mean that we study whether prediction methods are able to produce portfolios with large Sharpe ratios. In contrast, studying statistical significance in portfolio selection could mean that we study whether asset returns are predictable in the sense of the mean squared prediction error. Studying economic significance in option pricing could mean that we study whether hedging methods are able to well approximate the payoff of the option. In contrast, studying statistical significance in option pricing could mean that we study the goodness-of-fit of our underlying model for asset prices. Studying statistical significance can be important for understanding the underlying reasons for economic significance. However, the study of economic significance is of primary importance, and the study of statistical significance is of secondary importance.

A third theme of the book is the connections between the various parts of quantitative finance.
1. There are connections between risk management and portfolio selection: In portfolio selection, it is important to consider not only the expected returns but also the riskiness of the assets. In fact, the distinction between risk management and portfolio selection is not clear-cut.
2. There are connections between risk management and option pricing: The prices of options are largely influenced by the riskiness of the underlying assets.
3. There are connections between portfolio management and option pricing: Options are important assets to be included in a portfolio. In addition, multiperiod portfolio selection and option hedging can both be casted in the same mathematical framework.

Volatility prediction is useful in risk management, option pricing, and portfolio selection. Thus, volatility prediction is a constant topic throughout the book.
1.1 Statistical Finance

Statistical finance makes statistical analysis of financial and economic data.

Chapter 2 contains a description of the basic financial instruments, and it contains a description of the data sets that are analyzed in the book.

Chapter 3 studies univariate data analysis. We study univariate financial time series, but ignore the time series properties of data. A decomposition of a univariate distribution into the central part and into the tail parts is an important theme of the chapter.
1. We use different estimators for the central part and for the tails. Nonparametric density estimation is efficient at the center of a univariate distribution, but in the tails of the distribution the scarcity of data makes nonparametric estimation difficult. When we combine a nonparametric estimator for the central part and a parametric estimator for the tails then we obtain a semiparametric estimator for the distribution.
2. We use different visualization methods for the central part and for the tails. We apply two basic visualization tools: (1) kernel density estimates and (2) tail plots. Kernel density estimates can be used to visualize and to estimate the central part of the distribution. Tail plots are an empirical distribution based tool, and they can be used to visualize the tails of the distribution.

Chapter 4 studies multivariate data analysis. Multivariate data analysis considers simultaneously several time series, but the time series properties are ignored, and thus the analysis can be called cross-sectional. A basic concept is the copula, which makes it possible to compose a multivariate distribution into the part that describes the dependence and into the parts that describe the marginal distributions. We can estimate the marginal distributions using nonparametric methods, but to estimate dependence for a high-dimensional distribution it can be useful to apply parametric models. Combining nonparametric estimators of marginals and a parametric estimator of the copula leads to a semiparametric estimator of the distribution. Note that there is an analogy between the decomposition of a multivariate distribution into the copula and the marginals, and between the decomposition of a univariate distribution into the tails and the central area.

Chapter 5 studies time series analysis. Time series analysis adds the elements of dependence and time variation into the univariate and multivariate data analysis. Completely nonparametric time series modeling tends to become quite multidimensional, because dependence over consecutive time points leads to the estimation of a -dimensional distribution. However, a rather convenient method for time series analysis is obtained by taking as a starting point a univariate or a multivariate parametric model, and estimating the parameter using time localized smoothing. For example, we can apply time localized least squares or time localized maximum likelihood.

Chapter 6 studies prediction. Prediction is a central topic in time series analysis. The previous observations are used to predict the future observations. A distinction is made between moving average type of predictors and state space type of predictors. Both types of predictors can arise from parametric time series modeling: moving average and GARCH () models lead to moving average predictors, and autoregressive models lead to state space predictors. It is easy to construct nonparametric moving average predictors, and nonparametric regression analysis leads to nonparametric state space predictors.
1.2 Risk Management

Risk management studies measurement and management of financial risks. We concentrate on the market risk, which means the risk of unfavorable moves of asset prices.2

Chapter 7 studies volatility prediction. Prediction of volatility means in our terminology that the square of the return of a financial asset is predicted. The volatility prediction is extremely useful in almost every part of quantitative finance: we can apply volatility prediction in quantile estimation, and volatility prediction is an essential tool in option pricing and in portfolio selection. In addition, volatility prediction is needed when trading with variance products. We concentrate on the following three methods:
1. GARCH models are a classical and successful method to produce volatility predictions.
2. Exponentially weighted moving averages of squared returns lead to volatility predictions that are as good as GARCH () predictions.
3. Nonparametric state space smoothing leads to improvements of GARCH () predictions. We apply kernel regression with two explanatory variables: a moving average of squared returns and a moving average of returns. The response variable is a future squared return. A moving average of squared returns is in itself a good volatility predictor, but including a kernel regression on top of moving averages improves the predictions. In particular, we can take the leverage effect into account. The leverage effect means that when past returns have been low, then the future volatility tends to be higher, as compared to the future volatility when the past returns have been high.

Chapter 8 studies estimation of quantiles. The term value-at-risk is used to denote upper quantiles of a loss distribution of a financial asset. Value-at-risk at level has a direct interpretation in risk management: it is such value that the probability of losing more has a smaller probability than . We concentrate on the following three main classes of quantile estimators:
1. The empirical quantile estimator is a quantile of the empirical distribution. The empirical quantile estimator has many variants, since it can be used in conditional quantile estimation and it can be modified by kernel smoothing. In addition, empirical quantiles can be combined with volatility based and excess distribution based methods, since empirical quantiles can be used to estimate the quantiles of the residuals.
2. Volatility based quantile estimators apply a location-scale model. A volatility estimator leads directly to a quantile estimator, since estimation of the location is less important. The performance of volatility based quantile estimators depends on the choice of the base distribution, whose location and scale is estimated. However, in a time series setting the use of the empirical quantiles of the residuals provides a method that bypasses the problem of the choice of the base distribution.
3. Excess distribution based quantile estimators model the tail parametrically. These estimators ignore the central part of the distribution and model only the tail part parametrically. The tail part of the distribution is called the excess distribution. Extreme value theory can be used...
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