Mathematics and Statistics for Financial Risk Management

✍ Scribed by Michael B. Miller

• Publisher: Wiley
• Year: 2012
• Tongue: English
• Leaves: 305
• Series: Wiley Finance
• Category: Library

✦ Synopsis

A practical guide to modern financial risk management for both practitioners and academics The recent financial crisis and its impact on the broader economy underscore the importance of financial risk management in today's world. At the same time, financial products and investment strategies are becoming increasingly complex. Today, it is more important than ever that risk managers possess a sound understanding of mathematics and statistics. 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. Covers basic statistical concepts from volatility and Bayes' Law to regression analysis and hypothesis testing Introduces risk models, including Value-at-Risk, factor analysis, Monte Carlo simulations, and stress testing Explains time series analysis, including interest rate, GARCH, and jump-diffusion models Explores bond pricing, portfolio credit risk, optimal hedging, and many other financial risk topics If you're looking for a book that will help you understand the mathematics and statistics of financial risk management, look no further.

✦ Table of Contents

Mathematics and
Statistics for Financial
Risk Management......Page 3
Contents......Page 7
Preface......Page 11
Acknowledgments......Page 13
Logarithms......Page 15
Log Returns......Page 17
Compounding......Page 18
Graphing Log Returns......Page 19
Continuously Compounded Returns......Page 21
Combinatorics......Page 23
Discount Factors......Page 24
Geometric Series......Page 25
Problems......Page 31
Discrete Random Variables......Page 33
Continuous Random Variables......Page 34
Mutually Exclusive Events......Page 40
Independent Events......Page 41
Probability Matrices......Page 42
Conditional Probability......Page 44
Bayes’ Theorem......Page 45
Problems......Page 50
Averages......Page 53
Expectations......Page 60
Variance and Standard Deviation......Page 65
Covariance......Page 68
Correlation......Page 70
Application: Portfolio Variance and Hedging......Page 71
Skewness......Page 74
Kurtosis......Page 78
Coskewness and Cokurtosis......Page 81
Best Linear Unbiased Estimator (BLUE)......Page 85
Problems......Page 86
Uniform Distribution......Page 89
Bernoulli Distribution......Page 92
Binomial Distribution......Page 93
Poisson Distribution......Page 97
Normal Distribution......Page 98
Lognormal Distribution......Page 102
Central Limit Theorem......Page 104
Application: Monte Carlo Simulations Part I: Creating Normal Random Variables......Page 106
Chi-Squared Distribution......Page 108
Student’s t Distribution......Page 109
F-Distribution......Page 111
Mixture Distributions......Page 113
Problems......Page 116
The Sample Mean Revisited......Page 119
Sample Variance Revisited......Page 121
Confidence Intervals......Page 122
Hypothesis Testing......Page 123
Chebyshev’s Inequality......Page 127
Application: VaR......Page 128
Problems......Page 138
Matrix Notation......Page 141
Matrix Operations......Page 143
Application: Transition Matrices......Page 150
Application: Monte Carlo Simulations Part II: Cholesky Decomposition......Page 152
Problems......Page 155
Vectors Revisited......Page 157
Orthogonality......Page 160
Rotation......Page 166
Principal Component Analysis......Page 171
Application: The Dynamic Term Structure of Interest Rates......Page 176
Application: The Structure of Global Equity Markets......Page 181
Problems......Page 185
Linear Regression (One Regressor)......Page 187
Linear Regression (Multivariate)......Page 197
Application: Factor Analysis......Page 202
Application: Stress Testing......Page 206
Problems......Page 208
Random Walks......Page 211
Drift-Diffusion......Page 213
Autoregression......Page 214
Variance and Autocorrelation......Page 219
Stationarity......Page 220
Continuous Models......Page 226
Application: GARCH......Page 229
Application: Jump-Diffusion......Page 231
Application: Interest Rate Models......Page 232
Problems......Page 234
Mean......Page 237
Variance......Page 244
Weighted Least Squares......Page 245
Other Possibilities......Page 246
Application: Hybrid VaR......Page 247
Problems......Page 248
APPENDIX A Binary Numbers......Page 251
APPENDIX B Taylor Expansions......Page 253
APPENDIX C Vector Spaces......Page 255
APPENDIX D Greek Alphabet......Page 256
APPENDIX E Common Abbreviations......Page 257
Answers......Page 259
References......Page 297
About the Author......Page 299
Index......Page 301

✦ Subjects

Финансово-экономические дисциплины;Финансовый менеджмент;