The ideal primer on the mathematical and statistical concepts related to financial risk management While there are many good econometrics, statistics, and quant guides currently available, there is a surprising lack of practical insights on quantitative risk management. The quickest, easiest way to get a handle on the basics of financial risk management, this Second Edition of the popular guide fills that gap in the literature. Clear, concise, and brimming with real–world examples that vividly exemplify the concepts discussed, Mathematics and Statistics for Risk Management, Second Edition explains each concept, procedure, and formula from scratch. Throughout, it follows a consistent, quick–learning approach. As each technique is introduced, sample problems and discrete application sections demonstrate how the techniques can be applied to actual risk management problems. In addition, exercises at the end of each chapter and accompanying solutions found at the end of the book (also available online) allow you to practice the techniques covered and monitor your progress. 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 Explores bond pricing, portfolio credit risk, optimal hedging, and other key financial risk topics Now includes two new chapters covering Bayesian Analysis and Hypothesis Testing & Confidence Intervals, respectively If you?re eager to gain a firm understanding of the mathematics and statistics of financial risk management, this book is definitely for you. INDICE: 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 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 Triangular Distribution Beta Distribution Mixture Distributions Problems Chapter 5 Multivariate Distributions and Copulas Multivariate Distributions Copulas Problems Chapter 6 Bayesian Analysis Overview Bayes’ Theorem Bayes vs. Frequentists Many State Problems Continuous Distributions Bayesian Networks Bayesian Networks versus Correlation Matrices Problems Chapter 7 Hypothesis Testing & Confidence Intervals The Sample Mean Revisited Sample Variance Revisited Confidence Intervals Hypothesis Testing Chebyshev?s Inequality Application: VaR Problems Chapter 8 Matrix Algebra Matrix Notation Matrix Operations Application: Transition Matrices Application: Monte Carlo Simulations Part II: Cholesky Decomposition Problems Chapter 9 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 10 Linear Regression Analysis Linear Regression (One Regressor) Linear Regression (Multivariate) Application: Factor Analysis Application: Stress Testing Problems Chapter 11 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 12 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 Appendix F Copulas References About the Author About the Companion Website Index
- ISBN: 978-1-118-75029-2
- Editorial: John Wiley & Sons
- Encuadernacion: Cartoné
- Páginas: 336
- Fecha Publicación: 22/01/2014
- Nº Volúmenes: 1
- Idioma: Inglés