Mathematics and Statistics for Financial Risk Management
John Wiley & Sons Inc (Verlag)
978-1-118-17062-5 (ISBN)
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Mathematics and Statistics for Financial Risk Management is 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. This comprehensive resource covers basic statistical concepts from volatility and Bayes' Law to regression analysis and hypothesis testing.
Widely used risk models, including Value-at-Risk, factor analysis, Monte Carlo simulations, and stress testing are also explored. A chapter on time series analysis introduces interest rate modeling, GARCH, and jump-diffusion models. Bond pricing, portfolio credit risk, optimal hedging, and many other financial risk topics are covered as well. If you're looking for a book that will help you understand the mathematics and statistics of financial risk management, look no further.
Michael B. Miller studied economics at the American University of Paris and the University of Oxford before starting a career in finance. He has worked in risk management for more than ten years, most recently as the chief risk officer for a hedge fund in New York City.
Preface ix Acknowledgments xi CHAPTER 1 Some Basic Math 1 Logarithms 1 Log Returns 3 Compounding 4 Limited Liability 5 Graphing Log Returns 5 Continuously Compounded Returns 7 Combinatorics 9 Discount Factors 10 Geometric Series 11 Problems 16 CHAPTER 2 Probabilities 19 Discrete Random Variables 19 Continuous Random Variables 20 Mutually Exclusive Events 26 Independent Events 27 Probability Matrices 28 Conditional Probability 30 Bayes' Theorem 31 Problems 36 CHAPTER 3 Basic Statistics 39 Averages 39 Expectations 46 Variance and Standard Deviation 51 Standardized Variables 54 Covariance 54 Correlation 56 Application: Portfolio Variance and Hedging 57 Moments 60 Skewness 60 Kurtosis 64 Coskewness and Cokurtosis 67 Best Linear Unbiased Estimator (BLUE) 71 Problems 72 CHAPTER 4 Distributions 75 Parametric Distributions 75 Uniform Distribution 75 Bernoulli Distribution 78 Binomial Distribution 79 Poisson Distribution 83 Normal Distribution 84 Lognormal Distribution 88 Central Limit Theorem 90 Application: Monte Carlo Simulations Part I: Creating Normal Random Variables 92 Chi-Squared Distribution 94 Student's t Distribution 95 F -Distribution 97 Mixture Distributions 99 Problems 102 CHAPTER 5 Hypothesis Testing & Confidence Intervals 105 The Sample Mean Revisited 105 Sample Variance Revisited 107 Confidence Intervals 108 Hypothesis Testing 109 Chebyshev's Inequality 113 Application: VaR 114 Problems 124 CHAPTER 6 Matrix Algebra 127 Matrix Notation 127 Matrix Operations 129 Application: Transition Matrices 136 Application: Monte Carlo Simulations Part II: Cholesky Decomposition 138 Problems 141 CHAPTER 7 Vector Spaces 143 Vectors Revisited 143 Orthogonality 146 Rotation 152 Principal Component Analysis 157 Application: The Dynamic Term Structure of Interest Rates 162 Application: The Structure of Global Equity Markets 167 Problems 171 CHAPTER 8 Linear Regression Analysis 173 Linear Regression (One Regressor) 173 Linear Regression (Multivariate) 183 Application: Factor Analysis 188 Application: Stress Testing 192 Problems 194 CHAPTER 9 Time Series Models 197 Random Walks 197 Drift-Diffusion 199 Autoregression 200 Variance and Autocorrelation 205 Stationarity 206 Moving Average 212 Continuous Models 212 Application: GARCH 215 Application: Jump-Diffusion 217 Application: Interest Rate Models 218 Problems 220 CHAPTER 10 Decay Factors 223 Mean 223 Variance 230 Weighted Least Squares 231 Other Possibilities 232 Application: Hybrid VaR 233 Problems 234 APPENDIX A Binary Numbers 237 APPENDIX B Taylor Expansions 239 APPENDIX C Vector Spaces 241 APPENDIX D Greek Alphabet 242 APPENDIX E Common Abbreviations 243 Answers 245 References 283 About the Author 285 Index 287
| Reihe/Serie | Wiley Finance Series |
|---|---|
| Zusatzinfo | Illustrations |
| Verlagsort | New York |
| Sprache | englisch |
| Maße | 161 x 230 mm |
| Gewicht | 502 g |
| Einbandart | gebunden |
| Themenwelt | Wirtschaft ► Betriebswirtschaft / Management ► Finanzierung |
| Wirtschaft ► Volkswirtschaftslehre ► Ökonometrie | |
| ISBN-10 | 1-118-17062-8 / 1118170628 |
| ISBN-13 | 978-1-118-17062-5 / 9781118170625 |
| Zustand | Neuware |
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