Mathematics and Statistics for Financial Risk Management -- 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 -- Continuous Random Variables -- Mutually Exclusive Events -- Independent Events -- Probability Matrices -- Conditional Probability -- Bayes' Theorem -- Problems -- CHAPTER 3 Basic Statistics -- Averages -- Expectations -- Variance and Standard Deviation -- Standardized Variables -- Covariance -- Correlation -- Application: Portfolio Variance and Hedging -- Moments -- Skewness -- Kurtosis -- Coskewness and Cokurtosis -- Best Linear Unbiased Estimator (BLUE) -- Problems -- CHAPTER 4 Distributions -- Parametric Distributions -- Uniform Distribution -- Bernoulli Distribution -- Binomial Distribution -- Poisson Distribution -- Normal Distribution -- Lognormal Distribution -- Central Limit Theorem -- Application: Monte Carlo Simulations Part I: Creating Normal Random Variables -- Chi-Squared Distribution -- Student's t Distribution -- F-Distribution -- Mixture Distributions -- Problems -- CHAPTER 5 Hypothesis Testing & Confidence Intervals -- 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 Carlo Simulations Part II: Cholesky Decomposition -- Problems -- CHAPTER 7 Vector Spaces -- Vectors Revisited -- Orthogonality -- Rotation -- Principal Component Analysis -- Application: The Dynamic Term Structure of Interest Rates.

Application: The Structure of Global Equity Markets -- Problems -- CHAPTER 8 Linear Regression Analysis -- Linear Regression (One Regressor) -- Linear Regression (Multivariate) -- Application: Factor Analysis -- Application: Stress Testing -- Problems -- CHAPTER 9 Time Series Models -- Random Walks -- Drift-Diffusion -- Autoregression -- 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 A Binary Numbers -- APPENDIX B Taylor Expansions -- APPENDIX C Vector Spaces -- APPENDIX D Greek Alphabet -- APPENDIX E Common Abbreviations -- Answers -- References -- About the Author -- Index.