Mathematics and Statistics for Financial Risk Management.
Michael B. Miller
Bok Engelsk 2013 · Electronic books.
| Annen tittel | |
|---|---|
| Utgitt | Wiley
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| Omfang | 1 online resource (333 pages)
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| Utgave | 2nd ed.
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| Opplysninger | Intro -- Mathematics and Statistics for Financial Risk Management -- Contents -- Preface -- What's New in the Second Edition -- Acknowledgments -- Chapter 1 Some Basic Math -- Logarithms -- Log Returns -- Compounding -- Limited Liability -- Graphing Log Returns -- Continuously Compounded Returns -- Combinatorics -- Discount Factors -- Geometric Series -- Infinite Series -- Finite Series -- Problems -- Chapter 2 Probabilities -- Discrete Random Variables -- Continuous Random Variables -- Probability Density Functions -- Cumulative Distribution Functions -- Inverse Cumulative Distribution Functions -- Mutually Exclusive Events -- Independent Events -- Probability Matrices -- Conditional Probability -- Problems -- Chapter 3 Basic Statistics -- Averages -- Population and Sample Data -- Discrete Random Variables -- Continuous Random Variables -- Expectations -- Va riance 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 -- Discrete Distributions -- Continuous Distributions -- Visualization -- Correlation -- Marginal Distributions -- Copulas -- What Is a Copula? -- Graphing Copulas -- Using Copulas in Simulations.. - Appendix A Binary Numbers -- Appendix B Taylor Expansions -- Appendix C Vector Spaces -- Appendix D Greek Alphabet -- Appendix E Common Abbreviations -- Appendix F Copulas -- Answers -- Chapter 1 -- Chapter 2 -- Chapter 3 -- Chapter 4 -- Chapter 5 -- Chapter 6 -- Chapter 7 -- Chapter 8 -- Chapter 9 -- Chapter 10 -- Chapter 11 -- Chapter 12 -- References -- About the Author -- About the Companion Website -- Index.. - Parameterization of Copulas -- Problems -- Chapter 6 Bayesian Analysis -- Overview -- Bayes' Theorem -- Bayes versus Frequentists -- Many-State Problems -- Continuous Distributions -- Bayesian Networks -- Bayesian Networks versus Correlation Matrices -- Problems -- Chapter 7 Hypothesis Testing and Confidence Intervals -- Sample Mean Revisited -- Sample Variance Revisited -- Confidence Intervals -- Hypothesis Testing -- Which Way to Test? -- One Tail or Two? -- The Confidence Level Returns -- Chebyshev's Inequality -- Application: VaR -- Backtesting -- Subadditivity -- Expected Shortfall -- Problems -- Chapter 8 Matrix Algebra -- Matrix Notation -- Matrix Operations -- Addition and Subtraction -- Multiplication -- Zero Matrix -- Transpose -- 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) -- Ordinary Least Squares -- Estimating the Parameters -- Evaluating the Regression -- Linear Regression (Multivariate) -- Multicollinearity -- Estimating the Parameters -- Evaluating the Regression -- Application: Factor Analysis -- Application: Stress Testing -- Problems -- Chapter 11 Time Series Models -- Random Walks -- Drift-Diffusion Model -- Autoregression -- Variance and Autocorrelation -- Stationarity -- Moving Average -- Continuous Models -- Application: GARCH -- Application: Jump-Diffusion Model -- Application: Interest Rate Models -- Problems -- Chapter 12 Decay Factors -- Mean -- Variance -- Weighted Least Squares -- Other Possibilities -- Application: Hybrid VaR -- Problems.. - Mathematics and Statistics for Financial Risk Management is a practical guide to modern financial risk management for both practitioners and academics. Now 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. In 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. Mathematics and Statistics for Financial Risk Management is an indispensable reference for today's financial risk professional.
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| Emner | |
| Sjanger | |
| Dewey | |
| ISBN | 1-118-75029-2. - 1-306-20791-6
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