{"product_id":"mathematics-and-statistics-for-financial-risk-management-isbn-9781118750292","title":"Mathematics and Statistics for Financial Risk Management","description":"\u003cp\u003e\u003ci\u003eMathematics and Statistics for Financial Risk Management\u003c\/i\u003e is a practical guide to modern financial risk management for both practitioners and academics.\u003c\/p\u003e \u003cp\u003eNow in its second edition with more topics, more sample problems and more real world examples, this popular guide to financial risk management introduces readers to practical quantitative techniques for analyzing and managing financial risk.\u003c\/p\u003e \u003cp\u003eIn a concise and easy-to-read style, each chapter 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 Web site includes interactive Excel spreadsheet examples and templates.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eMathematics and Statistics for Financial Risk Management\u003c\/i\u003e is an indispensable reference for today’s financial risk professional.\u003c\/p\u003e \u003cp\u003ePreface ix\u003c\/p\u003e \u003cp\u003eWhat’s New in the Second Edition xi\u003c\/p\u003e \u003cp\u003eAcknowledgments xiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 1 Some Basic Math 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eLogarithms 1\u003c\/p\u003e \u003cp\u003eLog Returns 2\u003c\/p\u003e \u003cp\u003eCompounding 3\u003c\/p\u003e \u003cp\u003eLimited Liability 4\u003c\/p\u003e \u003cp\u003eGraphing Log Returns 5\u003c\/p\u003e \u003cp\u003eContinuously Compounded Returns 6\u003c\/p\u003e \u003cp\u003eCombinatorics 8\u003c\/p\u003e \u003cp\u003eDiscount Factors 9\u003c\/p\u003e \u003cp\u003eGeometric Series 9\u003c\/p\u003e \u003cp\u003eProblems 14\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2 Probabilities 15\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eDiscrete Random Variables 15\u003c\/p\u003e \u003cp\u003eContinuous Random Variables 15\u003c\/p\u003e \u003cp\u003eMutually Exclusive Events 21\u003c\/p\u003e \u003cp\u003eIndependent Events 22\u003c\/p\u003e \u003cp\u003eProbability Matrices 22\u003c\/p\u003e \u003cp\u003eConditional Probability 24\u003c\/p\u003e \u003cp\u003eProblems 26\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3 Basic Statistics 29\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAverages 29\u003c\/p\u003e \u003cp\u003eExpectations 34\u003c\/p\u003e \u003cp\u003eVariance and Standard Deviation 39\u003c\/p\u003e \u003cp\u003eStandardized Variables 41\u003c\/p\u003e \u003cp\u003eCovariance 42\u003c\/p\u003e \u003cp\u003eCorrelation 43\u003c\/p\u003e \u003cp\u003eApplication: Portfolio Variance and Hedging 44\u003c\/p\u003e \u003cp\u003eMoments 47\u003c\/p\u003e \u003cp\u003eSkewness 48\u003c\/p\u003e \u003cp\u003eKurtosis 51\u003c\/p\u003e \u003cp\u003eCoskewness and Cokurtosis 53\u003c\/p\u003e \u003cp\u003eBest Linear Unbiased Estimator (BLUE) 57\u003c\/p\u003e \u003cp\u003eProblems 58\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4 Distributions 61\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eParametric Distributions 61\u003c\/p\u003e \u003cp\u003eUniform Distribution 61\u003c\/p\u003e \u003cp\u003eBernoulli Distribution 63\u003c\/p\u003e \u003cp\u003eBinomial Distribution 65\u003c\/p\u003e \u003cp\u003ePoisson Distribution 68\u003c\/p\u003e \u003cp\u003eNormal Distribution 69\u003c\/p\u003e \u003cp\u003eLognormal Distribution 72\u003c\/p\u003e \u003cp\u003eCentral Limit Theorem 73\u003c\/p\u003e \u003cp\u003eApplication: Monte Carlo Simulations Part I: Creating Normal Random Variables 76\u003c\/p\u003e \u003cp\u003eChi-Squared Distribution 77\u003c\/p\u003e \u003cp\u003eStudent’s \u003ci\u003et\u003c\/i\u003e Distribution 78\u003c\/p\u003e \u003cp\u003e\u003ci\u003eF\u003c\/i\u003e-Distribution 79\u003c\/p\u003e \u003cp\u003eTriangular Distribution 81\u003c\/p\u003e \u003cp\u003eBeta Distribution 82\u003c\/p\u003e \u003cp\u003eMixture Distributions 83\u003c\/p\u003e \u003cp\u003eProblems 86\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5 Multivariate Distributions and Copulas 89\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eMultivariate Distributions 89\u003c\/p\u003e \u003cp\u003eCopulas 97\u003c\/p\u003e \u003cp\u003eProblems 111\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 6 Bayesian Analysis 113\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eOverview 113\u003c\/p\u003e \u003cp\u003eBayes’ Theorem 113\u003c\/p\u003e \u003cp\u003eBayes versus Frequentists 119\u003c\/p\u003e \u003cp\u003eMany-State Problems 120\u003c\/p\u003e \u003cp\u003eContinuous Distributions 124\u003c\/p\u003e \u003cp\u003eBayesian Networks 128\u003c\/p\u003e \u003cp\u003eBayesian Networks versus Correlation Matrices 130\u003c\/p\u003e \u003cp\u003eProblems 132\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 7 Hypothesis Testing and Confidence Intervals 135\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSample Mean Revisited 135\u003c\/p\u003e \u003cp\u003eSample Variance Revisited 137\u003c\/p\u003e \u003cp\u003eConfidence Intervals 137\u003c\/p\u003e \u003cp\u003eHypothesis Testing 139\u003c\/p\u003e \u003cp\u003eChebyshev’s Inequality 142\u003c\/p\u003e \u003cp\u003eApplication: VaR 142\u003c\/p\u003e \u003cp\u003eProblems 152\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 8 Matrix Algebra 155\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eMatrix Notation 155\u003c\/p\u003e \u003cp\u003eMatrix Operations 156\u003c\/p\u003e \u003cp\u003eApplication: Transition Matrices 163\u003c\/p\u003e \u003cp\u003eApplication: Monte Carlo Simulations Part II: Cholesky Decomposition 165\u003c\/p\u003e \u003cp\u003eProblems 168\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 9 Vector Spaces 169\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eVectors Revisited 169\u003c\/p\u003e \u003cp\u003eOrthogonality 172\u003c\/p\u003e \u003cp\u003eRotation 177\u003c\/p\u003e \u003cp\u003ePrincipal Component Analysis 181\u003c\/p\u003e \u003cp\u003eApplication: The Dynamic Term Structure of Interest Rates 185\u003c\/p\u003e \u003cp\u003eApplication: The Structure of Global Equity Markets 191\u003c\/p\u003e \u003cp\u003eProblems 193\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 10 Linear Regression Analysis 195\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eLinear Regression (One Regressor) 195\u003c\/p\u003e \u003cp\u003eLinear Regression (Multivariate) 203\u003c\/p\u003e \u003cp\u003eApplication: Factor Analysis 208\u003c\/p\u003e \u003cp\u003eApplication: Stress Testing 211\u003c\/p\u003e \u003cp\u003eProblems 212\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 11 Time Series Models 215\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eRandom Walks 215\u003c\/p\u003e \u003cp\u003eDrift-Diffusion Model 216\u003c\/p\u003e \u003cp\u003eAutoregression 217\u003c\/p\u003e \u003cp\u003eVariance and Autocorrelation 222\u003c\/p\u003e \u003cp\u003eStationarity 223\u003c\/p\u003e \u003cp\u003eMoving Average 227\u003c\/p\u003e \u003cp\u003eContinuous Models 228\u003c\/p\u003e \u003cp\u003eApplication: GARCH 230\u003c\/p\u003e \u003cp\u003eApplication: Jump-Diffusion Model 232\u003c\/p\u003e \u003cp\u003eApplication: Interest Rate Models 232\u003c\/p\u003e \u003cp\u003eProblems 234\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 12 Decay Factors 237\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eMean 237\u003c\/p\u003e \u003cp\u003eVariance 243\u003c\/p\u003e \u003cp\u003eWeighted Least Squares 244\u003c\/p\u003e \u003cp\u003eOther Possibilities 245\u003c\/p\u003e \u003cp\u003eApplication: Hybrid VaR 245\u003c\/p\u003e \u003cp\u003eProblems 247\u003c\/p\u003e \u003cp\u003eAppendix A Binary Numbers 249\u003c\/p\u003e \u003cp\u003eAppendix B Taylor Expansions 251\u003c\/p\u003e \u003cp\u003eAppendix C Vector Spaces 253\u003c\/p\u003e \u003cp\u003eAppendix D Greek Alphabet 255\u003c\/p\u003e \u003cp\u003eAppendix E Common Abbreviations 257\u003c\/p\u003e \u003cp\u003eAppendix F Copulas 259\u003c\/p\u003e \u003cp\u003eAnswers 263\u003c\/p\u003e \u003cp\u003eReferences 303\u003c\/p\u003e \u003cp\u003eAbout the Author 305\u003c\/p\u003e \u003cp\u003eAbout the Companion Website 307\u003c\/p\u003e \u003cp\u003eIndex 309\u003c\/p\u003e \u003cp\u003e\u003cb\u003eMichael B. Miller\u003c\/b\u003e studied economics at the American University of Paris and the University of Oxford before starting a career in finance. He is currently the CEO of Northstar Risk Corp. Before that, he was the Chief Risk Officer of Tremblant Capital Group, and prior to that, Head of Quantitative Risk Management at Fortress Investment Group. Mr. Miller is also a certified FRM and an adjunct professor at Rutgers Business School.\u003c\/p\u003e  \u003cp\u003e\u003ci\u003eMathematics and Statistics for Financial Risk Management\u003c\/i\u003e is a practical guide to modern financial risk management for both practitioners and academics. \u003c\/p\u003e \u003cp\u003eThe 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.  \u003c\/p\u003e\u003cp\u003eIn a concise and easy-to-read style, each chapter 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 web site includes interactive Excel spreadsheet examples and templates. \u003c\/p\u003e\u003cp\u003eThis comprehensive resource covers basic statistical concepts from standard deviation and correlation to regression analysis and hypothesis testing. Widely used risk models, including value at risk, factor analysis, Monte Carlo simulation, and stress testing are also explored. Time series analysis, interest rate modeling, optimal hedging, and many other financial topics are covered as well. \u003c\/p\u003e\u003cp\u003eThe \u003ci\u003eSecond Edition\u003c\/i\u003e of this popular guide includes two new chapters. The first new chapter, on multivariate distributions, explores important concepts for measuring the risk of portfolios, including joint distributions and copulas. The other new chapter, on Bayesian analysis, explores an approach to statistical analysis that is particularly useful in dealing with the short, noisy data sets that risk managers often face in practice.  \u003c\/p\u003e\u003cp\u003e\u003ci\u003eMathematics and Statistics for Financial Risk Management\u003c\/i\u003e is an indispensable reference for today’s financial risk professional.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989587837157,"sku":"NP9781118750292","price":110.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118750292.jpg?v=1761784710","url":"https:\/\/k12savings.com\/products\/mathematics-and-statistics-for-financial-risk-management-isbn-9781118750292","provider":"K12savings","version":"1.0","type":"link"}