Statistical finance: assessing the math in risk management (hardback) (series: wiley finance)

Praise for Mathematics and Statistics for Financial Risk Management

"This is the best book to date on the basic mathematics needed for financial risk management: clear, comprehensive, and up to date. Extensive examples and problems make clear how these concepts are used in the world"s top financial institutions. The book is perfect for self-study or classroom use." *Aaron Brown, author of Red-Blooded Risk, A World of Chance, and The Poker Face of Wall Street

"Risk managers have a need for relatively sophisticated mathematical tools in order to adequately describe and communicate the distributions of potential outcomes that they focus on every day. Michael Miller has provided a very nice, self-contained, practical introduction to the mathematics and statistics required for understanding the basic concepts of risk management." *Bob Litterman, Partner, Kepos Capital, and Executive Editor, Financial Analysts Journal

Mathematics and Statistics for Financial Risk Management is a practical guide to modern?financial risk management for both?practitioners and academic.

In a concise and easy-to-read style, each?chapter of this book introduces a different topic in mathematics or statistics.?As different techniques are introduced,?sample problems and application sections?demonstrate how these techniques can be?applied to actual risk management problems. Exercises at the end of each chapter and the accompanying solutions at the?end of the book allow readers to practice?the techniques they are learning and monitor their progress. A companion website?includes interactive Excel spreadsheet examples and templates.

Acknowledgments

Chapter 1: Some Basic Math

Logarithms

Log Returns

Compounding

Limited Liability

Graphing Log Returns

Continuously Compounded Returns

Combinatorics

Discount Factors

Geometric Series

Problems

Chapter 2: Probabilities

Discrete Random Variables

Mutually Exclusive Events

Independent Events

Probability Matrices

Conditional Probability

Bayes" Law

Problems

Chapter 3: Basic Statistics

Averages

Expectations

Variance and Standard Deviation

Standardized Variables

Covariance

Correlation

Moments

Skewness

Kurtosis

Coskewness and Cokurtosis

BLUE

Problems

Chapter 4: Distributions

Parametric Distributions

Uniform

Bernoulli

Binomial

Poisson Distribution

Normal

Lognormal

Central Limit Theorem

Chi-Squared Distribution

Student"s t Distribution

F-Distribution

Mixture Distributions

Problems

Chapter 5: Hypothesis Testing

The Sample Mean Revisited

Sample Variance Revisited

Confidence Intervals

Hypothesis Testing

Chebyshev"s Inequality

Application: VaR

Problems

Chapter 6: Matrix Algebra

Matrix Notation

Matrix Operations

Application: Transition Matrices

Application: Monte Carlool Simulations Part II: Cholesky Decomposition

Problems

Chapter 7: Vector Spaces

Vectors Revisited

Orthogonality

Rotation

Principal Component Analysis

Problems

Chapter 8: Linear Regression Analysis

Linear Regression (one regressor)

Optimal Hedging Revisited

Linear Regression (multivariate)

Application: Factor Analysis

Application: Stress Testing

Problems

Chapter 9: Time Series Models

Random Walks

Drift-Diffusion

Auto-regression

Variance and Autocorrelation

Stationarity

Moving Average

Continuous Models

Application: GARCH

Application: Jump-Diffusion

Application: Interest Rate Models

Problems

Chapter 10: Decay Factors

Mean

Variance

Weighted Least Squares

Other Possibilities

Application: Hybrid VaR

Problems

Appendix 1: Binary Numbers

Appendix 2: Taylor Expansions

Appendix 3: Vector Spaces

Appendix 4: Greek Alphabet

Appendix 5: Common Abbreviations

Answers

Bibliography

About the Author

Index