Produktbild: Mathematics and Statistics for Financial Risk Management
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Mathematics and Statistics for Financial Risk Management

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

07.02.2014

Verlag

John Wiley & Sons Inc

Seitenzahl

336

Maße (L/B/H)

26/18,3/2,3 cm

Gewicht

834 g

Auflage

2. Auflage

Sprache

Englisch

ISBN

978-1-118-75029-2

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

07.02.2014

Verlag

John Wiley & Sons Inc

Seitenzahl

336

Maße (L/B/H)

26/18,3/2,3 cm

Gewicht

834 g

Auflage

2. Auflage

Sprache

Englisch

ISBN

978-1-118-75029-2

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: GPSR Kontakt

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  • Produktbild: Mathematics and Statistics for Financial Risk Management
  • Preface ix

    What's New in the Second Edition xi

    Acknowledgments xiii

    Chapter 1 Some Basic Math 1

    Logarithms 1

    Log Returns 2

    Compounding 3

    Limited Liability 4

    Graphing Log Returns 5

    Continuously Compounded Returns 6

    Combinatorics 8

    Discount Factors 9

    Geometric Series 9

    Problems 14

    Chapter 2 Probabilities 15

    Discrete Random Variables 15

    Continuous Random Variables 15

    Mutually Exclusive Events 21

    Independent Events 22

    Probability Matrices 22

    Conditional Probability 24

    Problems 26

    Chapter 3 Basic Statistics 29

    Averages 29

    Expectations 34

    Variance and Standard Deviation 39

    Standardized Variables 41

    Covariance 42

    Correlation 43

    Application: Portfolio Variance and Hedging 44

    Moments 47

    Skewness 48

    Kurtosis 51

    Coskewness and Cokurtosis 53

    Best Linear Unbiased Estimator (BLUE) 57

    Problems 58

    Chapter 4 Distributions 61

    Parametric Distributions 61

    Uniform Distribution 61

    Bernoulli Distribution 63

    Binomial Distribution 65

    Poisson Distribution 68

    Normal Distribution 69

    Lognormal Distribution 72

    Central Limit Theorem 73

    Application: Monte Carlo Simulations Part I: Creating Normal Random Variables 76

    Chi-Squared Distribution 77

    Student's t Distribution 78

    F-Distribution 79

    Triangular Distribution 81

    Beta Distribution 82

    Mixture Distributions 83

    Problems 86

    Chapter 5 Multivariate Distributions and Copulas 89

    Multivariate Distributions 89

    Copulas 97

    Problems 111

    Chapter 6 Bayesian Analysis 113

    Overview 113

    Bayes' Theorem 113

    Bayes versus Frequentists 119

    Many-State Problems 120

    Continuous Distributions 124

    Bayesian Networks 128

    Bayesian Networks versus Correlation Matrices 130

    Problems 132

    Chapter 7 Hypothesis Testing and Confidence Intervals 135

    Sample Mean Revisited 135

    Sample Variance Revisited 137

    Confidence Intervals 137

    Hypothesis Testing 139

    Chebyshev's Inequality 142

    Application: VaR 142

    Problems 152

    Chapter 8 Matrix Algebra 155

    Matrix Notation 155

    Matrix Operations 156

    Application: Transition Matrices 163

    Application: Monte Carlo Simulations Part II: Cholesky Decomposition 165

    Problems 168

    Chapter 9 Vector Spaces 169

    Vectors Revisited 169

    Orthogonality 172

    Rotation 177

    Principal Component Analysis 181

    Application: The Dynamic Term Structure of Interest Rates 185

    Application: The Structure of Global Equity Markets 191

    Problems 193

    Chapter 10 Linear Regression Analysis 195

    Linear Regression (One Regressor) 195

    Linear Regression (Multivariate) 203

    Application: Factor Analysis 208

    Application: Stress Testing 211

    Problems 212

    Chapter 11 Time Series Models 215

    Random Walks 215

    Drift-Diffusion Model 216

    Autoregression 217

    Variance and Autocorrelation 222

    Stationarity 223

    Moving Average 227

    Continuous Models 228

    Application: GARCH 230

    Application: Jump-Diffusion Model 232

    Application: Interest Rate Models 232

    Problems 234

    Chapter 12 Decay Factors 237

    Mean 237

    Variance 243

    Weighted Least Squares 244

    Other Possibilities 245

    Application: Hybrid VaR 245

    Problems 247

    Appendix A Binary Numbers 249

    Appendix B Taylor Expansions 251

    Appendix C Vector Spaces 253

    Appendix D Greek Alphabet 255

    Appendix E Common Abbreviations 257

    Appendix F Copulas 259

    Answers 263

    References 303

    About the Author 305

    About the Companion Website 307

    Index 309