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Mathematics and statistics for financial risk management

Author: Michael B Miller
Publisher: Hoboken, New Jersey : Wiley, [2014]
Series: Wiley finance series.
Edition/Format:   Book : English : Second EditionView all editions and formats
"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  Read more...
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Additional Physical Format: Online version:
Miller, Michael B. (Michael Bernard), 1973-
Mathematics and statistics for financial risk management
Hoboken : Wiley, 2013
(DLC) 2013028163
Document Type: Book
All Authors / Contributors: Michael B Miller
ISBN: 9781118750292 1118750292
OCLC Number: 852763636
Description: xiii, 317 pages ; 27 cm.
Contents: Preface ix What's New in the Second Edition xi Acknowledgments xiii Chapter 1 Some Basic Math 1 Logarithms 1 Log Returns 2 Compounding 3 Limited Liability 4 Graphing Log Returns 5 Continuously Compounded Returns 6 Combinatorics 8 Discount Factors 9 Geometric Series 9 Problems 14 Chapter 2 Probabilities 15 Discrete Random Variables 15 Continuous Random Variables 15 Mutually Exclusive Events 21 Independent Events 22 Probability Matrices 22 Conditional Probability 24 Problems 26 Chapter 3 Basic Statistics 29 Averages 29 Expectations 34 Variance and Standard Deviation 39 Standardized Variables 41 Covariance 42 Correlation 43 Application: Portfolio Variance and Hedging 44 Moments 47 Skewness 48 Kurtosis 51 Coskewness and Cokurtosis 53 Best Linear Unbiased Estimator (BLUE) 57 Problems 58 Chapter 4 Distributions 61 Parametric Distributions 61 Uniform Distribution 61 Bernoulli Distribution 63 Binomial Distribution 65 Poisson Distribution 68 Normal Distribution 69 Lognormal Distribution 72 Central Limit Theorem 73 Application: Monte Carlo Simulations Part I: Creating Normal Random Variables 76 Chi-Squared Distribution 77 Student's t Distribution 78 F-Distribution 79 Triangular Distribution 81 Beta Distribution 82 Mixture Distributions 83 Problems 86 Chapter 5 Multivariate Distributions and Copulas 89 Multivariate Distributions 89 Copulas 97 Problems 111 Chapter 6 Bayesian Analysis 113 Overview 113 Bayes' Theorem 113 Bayes versus Frequentists 119 Many-State Problems 120 Continuous Distributions 124 Bayesian Networks 128 Bayesian Networks versus Correlation Matrices 130 Problems 132 Chapter 7 Hypothesis Testing and Confidence Intervals 135 Sample Mean Revisited 135 Sample Variance Revisited 137 Confidence Intervals 137 Hypothesis Testing 139 Chebyshev's Inequality 142 Application: VaR 142 Problems 152 Chapter 8 Matrix Algebra 155 Matrix Notation 155 Matrix Operations 156 Application: Transition Matrices 163 Application: Monte Carlo Simulations Part II: Cholesky Decomposition 165 Problems 168 Chapter 9 Vector Spaces 169 Vectors Revisited 169 Orthogonality 172 Rotation 177 Principal Component Analysis 181 Application: The Dynamic Term Structure of Interest Rates 185 Application: The Structure of Global Equity Markets 191 Problems 193 Chapter 10 Linear Regression Analysis 195 Linear Regression (One Regressor) 195 Linear Regression (Multivariate) 203 Application: Factor Analysis 208 Application: Stress Testing 211 Problems 212 Chapter 11 Time Series Models 215 Random Walks 215 Drift-Diffusion Model 216 Autoregression 217 Variance and Autocorrelation 222 Stationarity 223 Moving Average 227 Continuous Models 228 Application: GARCH 230 Application: Jump-Diffusion Model 232 Application: Interest Rate Models 232 Problems 234 Chapter 12 Decay Factors 237 Mean 237 Variance 243 Weighted Least Squares 244 Other Possibilities 245 Application: Hybrid VaR 245 Problems 247 Appendix A Binary Numbers 249 Appendix B Taylor Expansions 251 Appendix C Vector Spaces 253 Appendix D Greek Alphabet 255 Appendix E Common Abbreviations 257 Appendix F Copulas 259 Answers 263 References 303 About the Author 305 About the Companion Website 307 Index 309
Series Title: Wiley finance series.
Responsibility: Michael B. Miller.


Mathematics and Statistics for Financial Risk Management is a practical guide to modern financial risk management for both practitioners and academics.  Read more...
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