Probability and Statistics for Finance

by Rachev, Svetlozar T.; Hoechstoetter, Markus; Fabozzi, Frank J.; Focardi, Sergio M.

• ISBN13: 9780470400937
• ISBN10: 0470400935
• Edition: 1st
• Format: Hardcover
• Copyright: 2010-09-07
• Publisher: Wiley

Summary

In this book, the authors provide readers with an array of topics in probability and statistics for applying in the finance world. The book covers the basics through the intermediate applications typically not provided in a general statistics course for business majors. Even though these topics are not usually covered in MBA studies, they are becoming more and more important to finance practitioners in today's world. Rachev, Hoechstoetter, Fabozzi, and Focardi offer real-world illustrations throughout the text. Chapters include detailed discussions of Descriptive Statistics, Basic Probability Theory, Inductive Statistics, Multivariate Analysis, and Stochastic Processes.

Author Biography

SVETLOZAR T. RACHEV, PhD, DSC, is Chair Professor at the University of Karlsruhe in the School of Economics and Business Engineering, and Professor Emeritus at the University of California, Santa Barbara, in the Department of Statistics and Applied Probability. He was cofounder of Bravo Risk Management Group, acquired by FinAnalytica, where he currently serves as Chief Scientist.

MARKUS HÖCHSTÖTTER, PhD, is an Assistant Professor in the Department of Econometrics and Statistics, University of Karlsruhe.

FRANK J. FABOZZI, PhD, CFA, CPA, is Professor in the Practice of Finance and Becton Fellow at the Yale School of Management and Editor of the Journal of Portfolio Management. He is an Affiliated Professor at the University of Karlsruhe's Institute of Statistics, Econometrics and Mathematical Finance, and is on the Advisory Council for the Department of Operations Research and Financial Engineering at Princeton University.

SERGIO M. FOCARDI, PhD, is a Professor of Finance at EDHEC Business School and founding partner of the Paris-based consulting firm Intertek Group plc.

Table of Contents

Preface

About the Authors

Introduction

Probability Versus Statistics

Overview of the Book

Descriptive Statistics

Basic Data Analysis

Data Types

Frequency Distributions

Empirical Cumulative Frequency Distribution

Data Classes

Cumulative Frequency Distributions

Concepts Explained in this Chapter (In Order of Presentation)

Measures of Location and Spread

Parameters versus Statistics

Center and Location

Variation

Measures of the Linear Transformation

Summary of Measures

Concepts Explained in this Chapter (In Order of Presentation)

Graphical Representation of Data

Pie Charts

Bar Chart

Stem and Leaf Diagram

Frequency Histogram

Ogive Diagrams

Box Plot

QQ Plot

Concepts Explained in this Chapter (In Order of Presentation)

Multivariate Variables and Distributions

Data Tables and Frequencies

Class Data and Histograms

Marginal Distributions

Graphical Representation

Conditional Distribution

Conditional Parameters and Statistics

Independence

Covariance

Correlation

Contingency Coefficient

Concepts Explained in this Chapter (In Order of Presentation)

Introduction to Regression Analysis

The Role of Correlation

Regression Model: Linear Functional Relationship Between Two Variables

Distributional Assumptions of the Regression Model

Estimating the Regression Model

Goodness of Fit of the Model

Linear Regression of Some Non-Linear Relationship

Two Applications in Finance

Concepts Explained in this Chapter (In Order of Presentation)

Introduction to Time Series Analysis

What Is Time Series?

Decomposition of Time Series

Representation of Time Series with Difference Equations

Application: The Price Process

Concepts Explained in this Chapter (In Order of Presentation)

Basic Probability Theory

Concepts of Probability Theory

Historical Development of Alternative Approaches to Probability

Set Operations and Preliminaries

Probability Measure

Random Variable

Concepts Explained in this Chapter (In Order of Presentation)

Discrete Probability Distributions

Discrete Law

Bernoulli Distribution

Binomial Distribution

Hypergeometric Distribution

Multinomial Distribution

Poisson Distribution

Discrete Uniform Distribution

Concepts Explained in this Chapter (In Order of Presentation)

Continuous Probability Distributions

Continuous Probability Distribution Described

Distribution Function

Density Function

Continuous Random Variable

Computing Probabilities from the Density Function

Location Parameters

Dispersion Parameters

Concepts Explained in this Chapter (In Order of Presentation)

Continuous Probability Distributions with Appealing Statistical Properties

Normal Distribution

Chi-Square Distribution

Student's t-Distribution

F-Distribution

Exponential Distribution

Rectangular Distribution

Gamma Distribution

Beta Distribution

Log-Normal Distribution

Concepts Explained in this Chapter (In Order of Presentation)

Continuous Probability Distributions Dealing with Extreme Events

Generalized Extreme Value Distribution

Generalized Pareto Distribution

Normal Inverse Gaussian Distribution

a-Stable Distribution

Concepts Explained in this Chapter (In Order of Presentation)

Parameters of Location and Scale of Random Variables

Parameters of Location

Parameters of Scale

Concepts Explained in this Chapter (In Order of Presentation)

Appendix: Parameters for Various Distribution Functions

Joint Probability Distributions

Higher Dimensional Random Variables

Joint Probability Distribution

Marginal Distributions

Dependence

Covariance and Correlation

Selection of Multivariate Distributions

Concepts Explained in this Chapter (In Order of Presentation)

Conditional Probability and Bayes' Rule

Conditional Probability

Independent Events

Multiplicative Rule of Probability

Bayes' Rule

Conditional Parameters

Concepts Explained in this Chapter (In Order of Presentation)

Copula and Dependence Measures

Copula

Alternative Dependence Measures

Concepts Explained in this Chapter (In Order of Presentation)

Inductive Statistics

Point Estimators

Sample, Statistic, and Estimator

Quality Criteria of Estimators

Large Sample Criteria

Maximum Likehood Estimator

Exponential Family and Sufficiency

Concepts Explained in this Chapter (In Order of Presentation)

Confidence Intervals

Confidence Level and Confidence Interval

Confidence Interval for the Mean of a Normal Random Variable

Confidence Interval for the Mean of a Normal Random Variable with Unknown Variance

Confidence Interval for the Parameter p of a Binomial Distribution

Concepts Explained in this Chapter (In Order of Presentation)

Hypothesis Testing

Hypotheses

Error Types

Quality Criteria of a Test

Examples

Concepts Explained in this Chapter (In Order of Presentation)

Multivariate Linear Regression Analysis

Estimates and Diagnostics for Multivariate Linear Regression Analysis

The Multivariate Linear Regression Model

Assumptions of the Multivariate Linear Regression Model

Estimation of the Model Parameters

Designing the Model

Diagnostic Check and Model Significance

Applications to Finance

Concepts Explained in this Chapter (In Order of Presentation)

Designing and Building a Multivariate Linear Regression Model

The Problem of Multicollinearity

Incorporating Dummy Variables as Independent Variables

Model Building Techniques 561

Concepts Explained in this Chapter (In Order of Presentation)

Testing the Assumptions of the Multivariate Linear Regression Model

Tests for Linearity

Assumed Statistical Properties About the Error Term

Tests for the Residuals Being Normally Distributed

Tests for Constant Variance of the Error Term (Homoskedasticity)

Absence of Autocorrelation of the Residuals

Concepts Explained in this Chapter (In Order of Presentation)

Important Functions and Their Features

Continuous Function

Indicator Function

Derivatives

Monotonic Function

Integral

Some Functions

Fundamentals of Matrix Operations and Concepts

The Notion of Vector and Matrix

Matrix Multiplication

Particular Matrices

Positive Semidefinite Matrices

Binomial and Multinomial Coefficients

Binomial Coefficient

Multinomial Coefficient

Application of the Log-Normal Distribution to the Pricing of Call Options

Call Options

Deriving the Price of a European Call Option

Illustration

ReferenceS

Index

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