Produktbild: Mathematics and Statistics for Financial Risk Management

Mathematics and Statistics for Financial Risk Management

Aus der Reihe Wiley Finance Editions

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Verlag

Wiley

Seitenzahl

304

Maße (L/B/H)

23.8/16.6/2.6 cm

Gewicht

494 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-118-17062-5

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Verlag

Wiley

Seitenzahl

304

Maße (L/B/H)

23.8/16.6/2.6 cm

Gewicht

494 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-118-17062-5

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  • Produktbild: Mathematics and Statistics for Financial Risk Management
  • Preface ix
    Acknowledgments xi
    CHAPTER 1 Some Basic Math 1
    Logarithms 1
    Log Returns 3
    Compounding 4
    Limited Liability 5
    Graphing Log Returns 5
    Continuously Compounded Returns 7
    Combinatorics 9
    Discount Factors 10
    Geometric Series 11
    Problems 16
    CHAPTER 2 Probabilities 19
    Discrete Random Variables 19
    Continuous Random Variables 20
    Mutually Exclusive Events 26
    Independent Events 27
    Probability Matrices 28
    Conditional Probability 30
    Bayes' Theorem 31
    Problems 36
    CHAPTER 3 Basic Statistics 39
    Averages 39
    Expectations 46
    Variance and Standard Deviation 51
    Standardized Variables 54
    Covariance 54
    Correlation 56
    Application: Portfolio Variance and Hedging 57
    Moments 60
    Skewness 60
    Kurtosis 64
    Coskewness and Cokurtosis 67
    Best Linear Unbiased Estimator (BLUE) 71
    Problems 72
    CHAPTER 4 Distributions 75
    Parametric Distributions 75
    Uniform Distribution 75
    Bernoulli Distribution 78
    Binomial Distribution 79
    Poisson Distribution 83
    Normal Distribution 84
    Lognormal Distribution 88
    Central Limit Theorem 90
    Application: Monte Carlo Simulations Part I: Creating Normal Random Variables 92
    Chi-Squared Distribution 94
    Student's t Distribution 95
    F-Distribution 97
    Mixture Distributions 99
    Problems 102
    CHAPTER 5 Hypothesis Testing & Confidence Intervals 105
    The Sample Mean Revisited 105
    Sample Variance Revisited 107
    Confidence Intervals 108
    Hypothesis Testing 109
    Chebyshev's Inequality 113
    Application: VaR 114
    Problems 124
    CHAPTER 6 Matrix Algebra 127
    Matrix Notation 127
    Matrix Operations 129
    Application: Transition Matrices 136
    Application: Monte Carlo Simulations Part II: Cholesky Decomposition 138
    Problems 141
    CHAPTER 7 Vector Spaces 143
    Vectors Revisited 143
    Orthogonality 146
    Rotation 152
    Principal Component Analysis 157
    Application: The Dynamic Term Structure of Interest Rates 162
    Application: The Structure of Global Equity Markets 167
    Problems 171
    CHAPTER 8 Linear Regression Analysis 173
    Linear Regression (One Regressor) 173
    Linear Regression (Multivariate) 183
    Application: Factor Analysis 188
    Application: Stress Testing 192
    Problems 194
    CHAPTER 9 Time Series Models 197
    Random Walks 197
    Drift-Diffusion 199
    Autoregression 200
    Variance and Autocorrelation 205
    Stationarity 206
    Moving Average 212
    Continuous Models 212
    Application: GARCH 215
    Application: Jump-Diffusion 217
    Application: Interest Rate Models 218
    Problems 220
    CHAPTER 10 Decay Factors 223
    Mean 223
    Variance 230
    Weighted Least Squares 231
    Other Possibilities 232
    Application: Hybrid VaR 233
    Problems 234
    APPENDIX A Binary Numbers 237
    APPENDIX B Taylor Expansions 239
    APPENDIX C Vector Spaces 241
    APPENDIX D Greek Alphabet 242
    APPENDIX E Common Abbreviations 243
    Answers 245
    References 283
    About the Author 285
    Index 287