Mathematics and statistics for financial risk management / Michael B. Miller.

Format:

Book

Author/Creator:

Miller, Michael B. (Michael Bernard), 1973-

Series:

Wiley finance series.

Wiley finance series

Language:

English

Subjects (All):

Risk management--Mathematical models.

Risk management.

Risk management--Statistical methods.

Physical Description:

1 online resource (333 pages)

Edition:

Second edition.

Place of Publication:

Hoboken : Wiley, 2013.

Language Note:

English

Summary:

"This is an excellent book to grasp the basics of financial risk management. Everything in the book is explained from scratch and the concepts are very well exemplified with real life situations. Accompanied with a website filled with excel sheets for application, the book is great for future course material. This Second Edition of Mathematics and Statistics for Financial Risk Management includes 2 new chapters. The first chapter is on Bayesian Analysis and covers Bayes' Theorem, Many State Problems, Continuous Distributions, Bayesian Networks, and Bayesian Networks versus Correlation Matrices. The second new chapter is on Hypothesis Testing & Confidence Intervals and is on The Sample Mean Revisited, Sample Variance Revisited, Confidence Intervals, Hypothesis Testing, Chebyshev's Inequality, and Application: VaR. All chapters will have problems for testing and answers online"-- Provided by publisher.

Contents:

Intro

Mathematics and Statistics for Financial Risk Management

Contents

Preface

What's New in the Second Edition

Acknowledgments

Chapter 1 Some Basic Math

Logarithms

Log Returns

Compounding

Limited Liability

Graphing Log Returns

Continuously Compounded Returns

Combinatorics

Discount Factors

Geometric Series

Infinite Series

Finite Series

Problems

Chapter 2 Probabilities

Discrete Random Variables

Continuous Random Variables

Probability Density Functions

Cumulative Distribution Functions

Inverse Cumulative Distribution Functions

Mutually Exclusive Events

Independent Events

Probability Matrices

Conditional Probability

Chapter 3 Basic Statistics

Averages

Population and Sample Data

Expectations

Va riance and Standard Deviation

Standardized Variables

Covariance

Correlation

Application: Portfolio Variance and Hedging

Moments

Skewness

Kurtosis

Coskewness and Cokurtosis

Best Linear Unbiased Estimator (BLUE)

Chapter 4 Distributions

Parametric Distributions

Uniform Distribution

Bernoulli Distribution

Binomial Distribution

Poisson Distribution

Normal Distribution

Lognormal Distribution

Central Limit Theorem

Application: Monte Carlo Simulations Part I: Creating Normal Random Variables

Chi-Squared Distribution

Student's t Distribution

F-Distribution

Triangular Distribution

Beta Distribution

Mixture Distributions

Chapter 5 Multivariate Distributions and Copulas

Multivariate Distributions

Discrete Distributions

Continuous Distributions

Visualization

Marginal Distributions

Copulas

What Is a Copula?

Graphing Copulas

Using Copulas in Simulations.

Parameterization of Copulas

Chapter 6 Bayesian Analysis

Overview

Bayes' Theorem

Bayes versus Frequentists

Many-State Problems

Bayesian Networks

Bayesian Networks versus Correlation Matrices

Chapter 7 Hypothesis Testing and Confidence Intervals

Sample Mean Revisited

Sample Variance Revisited

Confidence Intervals

Hypothesis Testing

Which Way to Test?

One Tail or Two?

The Confidence Level Returns

Chebyshev's Inequality

Application: VaR

Backtesting

Subadditivity

Expected Shortfall

Chapter 8 Matrix Algebra

Matrix Notation

Matrix Operations

Addition and Subtraction

Multiplication

Zero Matrix

Transpose

Application: Transition Matrices

Application: Monte Carlo Simulations Part II: Cholesky Decomposition

Chapter 9 Vector Spaces

Vectors Revisited

Orthogonality

Rotation

Principal Component Analysis

Application: The Dynamic Term Structure of Interest Rates

Application: The Structure of Global Equity Markets

Chapter 10 Linear Regression Analysis

Linear Regression (One Regressor)

Ordinary Least Squares

Estimating the Parameters

Evaluating the Regression

Linear Regression (Multivariate)

Multicollinearity

Application: Factor Analysis

Application: Stress Testing

Chapter 11 Time Series Models

Random Walks

Drift-Diffusion Model

Autoregression

Variance and Autocorrelation

Stationarity

Moving Average

Continuous Models

Application: GARCH

Application: Jump-Diffusion Model

Application: Interest Rate Models

Chapter 12 Decay Factors

Mean

Variance

Weighted Least Squares

Other Possibilities

Application: Hybrid VaR

Problems.

Appendix A Binary Numbers

Appendix B Taylor Expansions

Appendix C Vector Spaces

Appendix D Greek Alphabet

Appendix E Common Abbreviations

Appendix F Copulas

Answers

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Chapter 11

Chapter 12

References

About the Author

About the Companion Website

Index.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed January 15, 2013).

ISBN:

9781118757536

111875753X

9781118757642

1118757645

9781118819616

1118819616

9781118757550

1118757556

OCLC:

852763676