Probability and Statistics for Finance
Published on 2. August 2010
672 pages
978-0-470-90630-9 (ISBN)
Description
A comprehensive look at how probability and statistics is appliedto the investment process
Finance has become increasingly more quantitative, drawing ontechniques in probability and statistics that many financepractitioners have not had exposure to before. In order to keep up,you need a firm understanding of this discipline.
Probability and Statistics for Finance addresses this issueby showing you how to apply quantitative methods to portfolios, andin all matter of your practices, in a clear, concise manner.Informative and accessible, this guide starts off with the basicsand builds to an intermediate level of mastery.
* Outlines an array of topics inprobability and statistics and how to apply them in the world offinance
* Includes detailed discussions ofdescriptive statistics, basic probability theory, inductivestatistics, and multivariate analysis
* Offers real-world illustrations of theissues addressed throughout the text
The authors cover a wide range of topics in this book, which can beused by all finance professionals as well as students aspiring toenter the field of finance.
More details
Other editions
Additional editions
Svetlozar T. Rachev | Markus Hoechstoetter | Frank J. Fabozzi
Probability and Statistics for Finance
Book
10/2010
Wiley
€93.00
Shipment within 10-20 days
Persons
SVETLOZAR T. RACHEV, PhD, DSC, is Chair Professor at theUniversity of Karlsruhe in the School of Economics and BusinessEngineering, and Professor Emeritus at the University ofCalifornia, Santa Barbara, in the Department of Statistics andApplied Probability. He was cofounder of Bravo Risk ManagementGroup, acquired by FinAnalytica, where he currently serves as ChiefScientist.
MARKUS HÖCHSTÖTTER, PhD, is an Assistant Professor inthe Department of Econometrics and Statistics, University ofKarlsruhe.
FRANK J. FABOZZI, PhD, CFA, CPA, is Professor in the Practice ofFinance and Becton Fellow at the Yale School of Management andEditor of the Journal of Portfolio Management. He is an AffiliatedProfessor at the University of Karlsruhe's Institute of Statistics,Econometrics and Mathematical Finance, and is on the AdvisoryCouncil for the Department of Operations Research and FinancialEngineering at Princeton University.
SERGIO M. FOCARDI, PhD, is a Professor of Finance at EDHECBusiness School and founding partner of the Paris-based consultingfirm Intertek Group plc.
Content
- Intro
- Probability and Statistics for Finance
- Contents
- Preface
- About the Authors
- CHAPTER 1 Introduction
- PROBABILITY VS. STATISTICS
- OVERVIEW OF THE BOOK
- Part One: Descriptive Statistics
- Part Two: Basic Probability Theory
- Part Three: Inductive Statistics
- Part Four: Multivariate Linear Regression
- Appendixes
- PART One Descriptive Statistics
- CHAPTER 2 Basic Data Analysis
- DATA TYPES
- How To Obain Data
- The Information Contained in the Data
- Data Levels and Scale
- Cross-Sectional Data and Time Series
- FREQUENCY DISTRIBUTIONS
- Sorting and Counting Data
- Formal Presentation of Frequency
- EMPIRICAL CUMULATIVE FREQUENCY DISTRIBUTION
- Accumulating Frequencies
- Formal Presentation of Cumulative Frequency Distributions
- DATA CLASSES
- Reasons for Classifying
- Formal Procedure for Classifying
- Example of Classifying Procedures
- CUMULATIVE FREQUENCY DISTRIBUTIONS
- CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
- CHAPTER 3 Measures of Location and Spread
- PARAMETERS VS. STATISTICS
- CENTER AND LOCATION
- Mean
- Median
- Mode
- Weighted Mean
- Quantiles
- VARIATION
- Range
- Interquartile Range
- Absolute Deviation
- Variance and Standard Deviation
- Skewness
- Data Levels and Measures of Variation
- Empirical Rule
- Coefficient of Variation and Standardization
- MEASURES OF THE LINEAR TRANSFORMATION
- SUMMARY OF MEASURES
- CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
- CHAPTER 4 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)
- CHAPTER 5 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)
- CHAPTER 6 Introduction to Regression Analysis
- THE ROLE OF CORRELATION
- Stock Return Example
- Correlation in Finance
- REGRESSION MODEL: LINEAR FUNCTIONAL RELATIONSHIP BETWEEN TWO VARIABLES
- DISTRIBUTIONAL ASSUMPTIONS OF THE REGRESSION MODEL
- ESTIMATING THE REGRESSION MODEL
- Application to Stock Returns
- GOODNESS OF FIT OF THE MODEL
- Relationship between Coefficient of Determination and Correlation Coefficient
- LINEAR REGRESSION OF SOME NONLINEAR RELATIONSHIP
- Linear Regression of Exponential Data
- TWO APPLICATIONS IN FINANCE
- Characteristic Line
- Application to Hedging
- CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
- CHAPTER 7 Introduction to Time Series Analysis
- WHAT IS TIME SERIES?
- DECOMPOSITION OF TIME SERIES
- Application to S&P 500 Index Returns
- REPRESENTATION OF TIME SERIES WITH DIFFERENCE EQUATIONS
- APPLICATION: THE PRICE PROCESS
- Random Walk
- Error Correction
- CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
- PART Two Basic Probability Theory
- CHAPTER 8 Concepts of Probability Theory
- HISTORICAL DEVELOPMENT OF ALTERNATIVE APPROACHES TO PROBABILITY
- Probability as Relative Frequencies
- Axiomatic System
- SET OPERATIONS AND PRELIMINARIES
- Set Operations
- Right-Continuous and Nondecreasing Functions
- Outcome, Space, and Events
- The Measurable Space
- PROBABILITY MEASURE
- RANDOM VARIABLE
- Random Variables on a Countable Space
- Random Variables on an Uncountable Space
- CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
- CHAPTER 9 Discrete Probability Distributions
- DISCRETE LAW
- Random Variable on the Countable Space
- Mean and Variance
- BERNOULLI DISTRIBUTION
- BINOMIAL DISTRIBUTION
- Application to the Binomial Stock Price Model
- Application to the Binomial Interest Rate Model
- Application to the Binomial Default Distribution Model
- HYPERGEOMETRIC DISTRIBUTION
- Application
- MULTINOMIAL DISTRIBUTION
- Multinomial Stock Price Model
- POISSON DISTRIBUTION
- Application to Credit Risk Modeling for a Bond Portfolio
- DISCRETE UNIFORM DISTRIBUTION
- Application to the Multinomial Stock Price Model
- CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
- CHAPTER 10 Continuous Probability Distributions
- CONTINUOUS PROBABILITY DISTRIBUTION DESCRIBED
- DISTRIBUTION FUNCTION
- DENSITY FUNCTION
- Requirements on the Density Function
- CONTINUOUS RANDOM VARIABLE
- COMPUTING PROBABILITIES FROM THE DENSITY FUNCTION
- LOCATION PARAMETERS
- DISPERSION PARAMETERS
- Moments of Higher Order
- CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
- CHAPTER 11 Continuous Probability Distributions with Appealing Statistical Properties
- NORMAL DISTRIBUTION
- Properties of the Normal Distribution
- Applications to Stock Returns
- CHI-SQUARE DISTRIBUTION
- Application to Modeling Short-Term Interest Rates
- STUDENT'S t-DISTRIBUTION
- Application to Stock Returns
- F -DISTRIBUTION
- EXPONENTIAL DISTRIBUTION
- Applications in Finance
- RECTANGULAR DISTRIBUTION
- GAMMA DISTRIBUTION
- Erlang Distribution
- BETA DISTRIBUTION
- LOG-NORMAL DISTRIBUTION
- Application to Modeling Asset Returns
- CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
- CHAPTER 12 Continuous Probability Distributions Dealing with Extreme Events
- GENERALIZED EXTREME VALUE DISTRIBUTION
- GENERALIZED PARETO DISTRIBUTION
- NORMAL INVERSE GAUSSIAN DISTRIBUTION
- Normal Distribution versus Normal Inverse Gaussian Distribution
- a-STABLE DISTRIBUTION
- CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
- CHAPTER 13 Parameters of Location and Scale of Random Variables
- PARAMETERS OF LOCATION
- Quantiles
- Mode
- Mean (First Moment)
- PARAMETERS OF SCALE
- Moments of Higher Order
- Variance
- Standard Deviation
- Skewness
- Kurtosis
- Kurtosis of the GE Daily Returns
- CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
- CHAPTER 14 Joint Probability Distributions
- HIGHER DIMENSIONAL RANDOM VARIABLES
- Discrete Case
- Continuous Case
- JOINT PROBABILITY DISTRIBUTION
- Discrete Case
- Continuous Case
- MARGINAL DISTRIBUTIONS
- Discrete Case
- Continuous Case
- DEPENDENCE
- Discrete Case
- Continuous Case
- COVARIANCE AND CORRELATION
- Discrete Case
- Continuous Case
- Aspects of the Covariance and Covariance Matrix
- Correlation
- Criticism of the Correlation and Covariance as a Measure of Joint Randomness
- SELECTION OF MULTIVARIATE DISTRIBUTIONS
- Multivariate Normal Distribution
- Multivariate t-Distribution
- Elliptical Distributions
- CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
- CHAPTER 15 Conditional Probability and Bayes' Rule
- CONDITIONAL PROBABILITY
- Formula for Conditional Probability
- INDEPENDENT EVENTS
- MULTIPLICATIVE RULE OF PROBABILITY
- Illustration: The Multiplicative Rule of Probability
- Multiplicative Rule of Probability for Independent Events
- Law of Total Probability
- Illustration: The Law of Total Probability
- The Law of Total Probability for More than Two Events
- BAYES' RULE
- Illustration: Application of Bayes' Rule
- CONDITIONAL PARAMETERS
- Conditional Expectation
- Conditional Variance
- Expected Tail Loss
- CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
- CHAPTER 16 Copula and Dependence Measures
- COPULA
- Construction of the Copula
- Specifications of the Copula
- Properties of the Copula
- Simulation of Financial Returns Using the Copula
- The Copula for Two Dimensions
- Simulation with the Gaussian Copula (d = 2)
- ALTERNATIVE DEPENDENCE MEASURES
- Rank Correlation Measures
- Tail Dependence
- CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
- PART Three Inductive Statistics
- CHAPTER 17 Point Estimators
- SAMPLE, STATISTIC, AND ESTIMATOR
- Sample
- Sampling Techniques
- Illustrations of Drawing with Replacement
- Statistic
- Estimator
- Estimator for the Mean
- Linear Estimators
- Estimating the Parameter p of the Bernoulli Distribution
- Estimating the Parameter of Poisson Distribution
- Linear Estimator with Lags
- QUALITY CRITERIA OF ESTIMATORS
- Bias
- Bias of the Sample Mean
- Bias of the Sample Variance
- Mean-Square Error
- Mean-Square Error of the Sample Mean
- Mean-Square Error of the Variance Estimator
- LARGE SAMPLE CRITERIA
- Consistency
- Consistency of the Sample Mean of Normally Distributed Data
- Consistency of the Variance Estimator
- Unbiased Efficiency
- Efficiency of the Sample Mean
- Efficiency of the Bias Corrected Sample Variance
- Linear Unbiased Estimators
- MAXIMUM LIKEHOOD ESTIMATOR
- MLE of the Parameter of the Poisson Distribution
- MLE of the Parameter of the Exponential Distribution
- MLE of the Parameter Components of the Normal Distribution
- Cramér-Rao Lower Bound
- Cramér-Rao Bound of the MLE of Parameter of the Exponential Distribution
- Cramér-Rao Bounds of the MLE of the Parameters of the Normal Distribution
- EXPONENTIAL FAMILY AND SUFFICIENCY
- Exponential Family
- Exponential Family of the Poisson Distribution
- Exponential Family of the Exponential Distribution
- Exponential Family of the Normal Distribution
- Sufficiency
- Sufficient Statistic for the Parameter of the Poisson Distribution
- CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
- CHAPTER 18 Confidence Intervals
- CONFIDENCE LEVEL AND CONFIDENCE INTERVAL
- Definition of a Confidence Level
- Definition and Interpretation of a 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 VARIANCE OF A NORMAL RANDOM VARIABLE
- CONFIDENCE INTERVAL FOR THE VARIANCE OF A NORMAL RANDOM VARIABLE WITH UNKNOWN MEAN
- CONFIDENCE INTERVAL FOR THE PARAMETER P OF A BINOMIAL DISTRIBUTION
- CONFIDENCE INTERVAL FOR THE PARAMETER ? OF AN EXPONENTIAL DISTRIBUTION
- CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
- CHAPTER 19 Hypothesis Testing
- HYPOTHESES
- Setting Up the Hypotheses
- Decision Rule
- ERROR TYPES
- Type I and Type II Error
- Test Size
- The p-Value
- QUALITY CRITERIA OF A TEST
- Power of a Test
- Unbiased Test
- Consistent Test
- EXAMPLES
- Simple Test for Parameter of the Poisson Distribution
- One-Tailed Test for Parameter of Exponential Distribution
- One-Tailed Test for µ of the Normal Distribution When s2 Is Known
- One-Tailed Test for s2 of the Normal Distribution When µ Is Known
- Two-Tailed Test for the Parameter µ of the Normal Distribution When s2 Is Known
- Equal Tails Test for the Parameter s2 of the Normal Distribution When µ Is Known
- Test for Equality of Means
- Two-Tailed Kolmogorov-Smirnov Test for Equality of Distribution
- Likelihood Ratio Test
- CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
- PART Four Multivariate Linear Regression Analysis
- CHAPTER 20 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
- Testing for the Significance of the Model
- Testing for the Significance of the Independent Variables
- The F-Test for Inclusion of Additional Variables
- APPLICATIONS TO FINANCE
- Estimation of Empirical Duration
- Predicting the 10-Year Treasury Yield
- CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
- CHAPTER 21 Designing and Building a Multivariate Linear Regression Model
- THE PROBLEM OF MULTICOLLINEARITY
- Procedures for Mitigating Multicollinearity
- INCORPORATING DUMMY VARIABLES AS INDEPENDENT VARIABLES
- Application to Testing the Mutual Fund Characteristic Lines in Different Market Environments
- Application to Predicting High-Yield Corporate Bond Spreads
- MODEL BUILDING TECHNIQUES
- Stepwise Inclusion Method
- Stepwise Exclusion Method
- Standard Stepwise Regression Method
- CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
- CHAPTER 22 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
- Chi-Square Statistic
- Jarque-Bera Test Statistic
- Analysis of Standardized Residuals
- TESTS FOR CONSTANT VARIANCE OF THE ERROR TERM (HOMOSKEDASTICITY)
- Modeling to Account for Heteroskedasticity
- ABSENCE OF AUTOCORRELATION OF THE RESIDUALS
- Detecting Autocorrelation
- Modeling in the Presence of Autocorrelation
- Autoregressive Moving Average Models
- CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION)
- APPENDIX A Important Functions and Their Features
- CONTINUOUS FUNCTION
- General Idea
- Formal Derivation
- INDICATOR FUNCTION
- DERIVATIVES
- Construction of the Derivative
- MONOTONIC FUNCTION
- INTEGRAL
- Approximation of the Area through Rectangles
- Relationship Between Integral and Derivative
- SOME FUNCTIONS
- Factorial
- Gamma Function
- Beta Function
- Bessel Function of the Third Kind
- Characteristic Function
- APPENDIX B Fundamentals of Matrix Operations and Concepts
- THE NOTION OF VECTOR AND MATRIX
- MATRIX MULTIPLICATION
- PARTICULAR MATRICES
- Determinant of a Matrix
- Eigenvalues and Eigenvectors
- POSITIVE SEMIDEFINITE MATRICES
- APPENDIX C Binomial and Multinomial Coefficients
- BINOMIAL COEFFICIENT
- Derivation of the Binomial Coefficient
- MULTINOMIAL COEFFICIENT
- APPENDIX D 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
- EULA
