Mathematics and Statistics for Financial Risk Management / Edition 1

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Overview

In chapter 1, there is a review three math topics -- logarithms, combinatorics, and geometric series – and one financial topic, discount factors. Emphasis will be given to the specific aspects of these topics that are most relevant to risk management. In chapter 2, the author explores the application of probabilities to risk management. There is also an introduction to basic terminology and notations that will be used throughout the rest of the book. In chapter 3, Miller teaches how to describe a collection of data in precise statistical terms. Many of the concepts will be familiar, but the notation and terminology might be new. This notation and terminology will be used throughout the rest of the book. In chapter 4, some of the most common probability distributions will be pointed out, followed by a chapter on two closely related topics, confidence intervals and hypothesis testing. For risk management, these are possibly the two most important concepts in statistics. Chapter 6 provides a basic introduction to linear regression models. At the end of the chapter, Miller explores two risk management applications, factor analysis and stress testing. The final chapter is on a class of estimators, which has become very popular in finance and risk management for analyzing historical data. These models hint at the limitations of the type of analysis that we have been explores in previous chapters. This book has a lot of charts and equations.
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Editorial Reviews

From the Publisher
"At every turn this book shows the relevance of mathematical and statistical concepts to risk management. They are no longer the desiccated notions found in most textbooks but assume a sense of vibrancy. So, if you're trying to hone your skills, this book is a great place to start." (SeekingAlpha, April 2012)
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Product Details

  • ISBN-13: 9781118170625
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 3/6/2012
  • Series: Wiley Finance Series , #723
  • Edition number: 1
  • Pages: 304
  • Product dimensions: 6.30 (w) x 9.10 (h) x 1.10 (d)

Meet the Author

Michael B. Miller studied economics at the American University of Paris and the University of Oxford before starting a career in finance. He is currently the CEO of Northstar Risk Corp. Before that, he was the Chief Risk Officer of Tremblant Capital Group, and prior to that, Head of Quantitative Risk Management at Fortress Investment Group. Mr. Miller is also a certified FRM and an adjunct professor at Rutgers Business School.

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Table of Contents

Preface

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

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