Carol Alexander is a Professor of Risk Management at the ICMA Centre, University of Reading, and Chair of the Academic Advisory Council of the Professional Risk Manager's International Association (PRMIA). She is the author of Market Models: A Guide to Financial Data Analysis(John Wiley & Sons Ltd, 2001) and has been editor and contributor of a very large number of books in finance and mathematics, including the multi-volume Professional Risk Manager's Handbook(McGraw-Hill, 2008 and PRMIA Publications). Carol has published nearly 100 academic journal articles, book chapters and books, the majority of which focus on financial risk management and mathematical finance.
Professor Alexander is one of the world's leading authorities on market risk analysis. For further details, see [...]

List of Figures xiii

List of Tables xvi

List of Examples xvii

Foreword xix

Preface to Volume I xxiii

I.1 Basic Calculus for Finance 1

I.1.1 Introduction 1

I.1.2 Functions and Graphs, Equations and Roots 3

I.1.3 Differentiation and Integration 10

I.1.4 Analysis of Financial Returns 16

I.1.5 Functions of Several Variables 26

I.1.6 Taylor Expansion 31

I.1.7 Summary and Conclusions 35

I.2 Essential Linear Algebra for Finance 37

I.2.1 Introduction 37

I.2.2 Matrix Algebra and its Mathematical Applications 38

I.2.3 Eigenvectors and Eigenvalues 48

I.2.4 Applications to Linear Portfolios 55

I.2.5 Matrix Decomposition 61

I.2.6 Principal Component Analysis 64

I.2.7 Summary and Conclusions 70

I.3 Probability and Statistics 71

I.3.1 Introduction 71

I.3.2 Basic Concepts 72

I.3.3 Univariate Distributions 85

I.3.4 Multivariate Distributions 107

I.3.5 Introduction to Statistical Inference 118

I.3.6 Maximum Likelihood Estimation 130

I.3.7 Stochastic Processes in Discrete and Continuous Time 134

I.3.8 Summary and Conclusions 140

I.4 Introduction to Linear Regression 143

I.4.1 Introduction 143

I.4.2 Simple Linear Regression 144

I.4.3 Properties of OLS Estimators 155

I.4.4 Multivariate Linear Regression 158

I.4.5 Autocorrelation and Heteroscedasticity 175

I.4.6 Applications of Linear Regression in Finance 179

I.4.7 Summary and Conclusions 184

I.5 Numerical Methods in Finance 185

I.5.1 Introduction 185

I.5.2 Iteration 187

I.5.3 Interpolation and Extrapolation 193

I.5.4 Optimization 200

I.5.5 Finite Difference Approximations 206

I.5.6 Binomial Lattices 210

I.5.7 Monte Carlo Simulation 217

I.5.8 Summary and Conclusions 223

I.6 Introduction to Portfolio Theory 225

I.6.1 Introduction 225

I.6.2 Utility Theory 226

I.6.3 Portfolio Allocation 237

I.6.4 Theory of Asset Pricing 250

I.6.5 Risk Adjusted Performance Measures 256

I.6.6 Summary and Conclusions 266

References 269

Statistical Tables 273

Index 279