Probability and Statistics for Finance

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.

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.

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
Table of Contents provided by Publisher. All Rights Reserved.

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Probability and Statistics for Finance

Summary

Author Biography

Table of Contents

Supplemental Materials