Mathematics and statistics for financial risk management
Miller, Michael B. (Michael Bernard)
1973-
creator
text
bibliography
Electronic books.
nju
Hoboken, N.J
Wiley
2012
monographic
eng
1 online resource (xi, 281 pages) : illustrations.
"In chapter 1, there is a review three math topics -- logarithms, combinatorics, and geometric series - and one financial topic, discount factors. Emphasis will be given to the specific aspects of these topics that are most relevant to risk management. In chapter 2, the author explores the application of probabilities to risk management. There is also an introduction to basic terminology and notations that will be used throughout the rest of the book. In chapter 3, Miller teaches how to describe a collection of data in precise statistical terms. Many of the concepts will be familiar, but the notation and terminology might be new. This notation and terminology will be used throughout the rest of the book. In chapter 4, some of the most common probability distributions will be pointed out, followed by a chapter on two closely related topics, confidence intervals and hypothesis testing. For risk management, these are possibly the two most important concepts in statistics. Chapter 6 provides a basic introduction to linear regression models. At the end of the chapter, Miller explores two risk management applications, factor analysis and stress testing. The final chapter is on a class of estimators, which has become very popular in finance and risk management for analyzing historical data. These models hint at the limitations of the type of analysis that we have been explores in previous chapters. This book has a lot of charts and equations"--
Some basic math -- Probabilities -- Basic statistics -- Distribution -- Hypothesis testing & confidence intervals -- Matrix algebra -- Vector spaces -- Linear regression analysis -- Time series models -- Decay factors.
Mathematics andStatistics for FinancialRisk 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 VariablesCovariance; 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 IntervalsThe 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 AnalysisLinear 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 ExpansionsAPPENDIX C Vector Spaces; APPENDIX D Greek Alphabet; APPENDIX E Common Abbreviations; Answers; References; About the Author; Index.
Michael B. Miller.
Includes bibliographical references and index.
Risk management
Mathematical models
Risk management
Statistical methods
Reference & resource series
BUSINESS & ECONOMICS
Finance
Business
HD61 .M537 2012eb
332.01/5195
BUS027000
Mathematics and statistics for financial risk management
Miller, Michael B.
Hoboken, N.J. : Wiley, 2012
(DLC) 2011039256
Wiley finance series
9781118227770
1118227778
9781118239766
1118239768
1280588969
9781280588969
9781118819616
1118819616
1306207916
9781306207911
EB00088118 Recorded Books
361879 MIL
http://onlinelibrary.wiley.com/book/10.1002/9781118819616
http://onlinelibrary.wiley.com/book/10.1002/9781118819616
E7B
110923
20171224113922.0
ocn785777914
eng