Market Risk Analysis, Volume I, Quantitative Methods in Finance
All together, the Market Risk Analysis four volume set illustrates virtually every concept or formula with a practical, numerical example or a longer, empirical case study. Across all four volumes there are approximately 300 numerical and empirical examples, 400 graphs and figures and 30 case studies many of which are contained in interactive Excel spreadsheets available from the accompanying CD-ROM . Empirical examples and case studies specific to this volume include:
Principal component analysis of European equity indices;
Calibration of Student t distribution by maximum likelihood;
Orthogonal regression and estimation of equity factor models;
Simulations of geometric Brownian motion, and of correlated Student t variables;
Pricing European and American options with binomial trees, and European options with the Black-Scholes-Merton formula;
Cubic spline fitting of yields curves and implied volatilities;
Solution of Markowitz problem with no short sales and other constraints;
Calculation of risk adjusted performance metrics including generalised Sharpe ratio, omega and kappa indices.
List of Tables.
List of Examples.
Preface to Volume 1.
I.1 Basic Calculus for Finance.
I.1.2 Functions and Graphs, Equations and Roots.
I.1.3 Differentiation and Integration.
I.1.4 Analysis of Financial Returns.
I.1.5 Functions of Several Variables.
I.1.6 Taylor Expansion.
I.1.7 Summary and Conclusions.
I.2 Essential Linear Algebra for Finance.
I.2.2 Matrix Algebra and its Mathematical Applications.
I.2.3 Eigenvectors and Eigenvalues.
I.2.4 Applications to Linear Portfolios.
I.2.5 Matrix Decomposition.
I.2.6 Principal Component Analysis.
I.2.7 Summary and Conclusions.
I.3 Probability and Statistics.
I.3.2 Basic Concepts.
I.3.3 Univariate Distributions.
I.3.4 Multivariate Distributions.
I.3.5 Introduction to Statistical Inference.
I.3.6 Maximum Likelihood Estimation.
I.3.7 Stochastic Processes in Discrete and Continuous Time.
I.3.8 Summary and Conclusions.
I.4 Introduction to Linear Regression.
I.4.2 Simple Linear Regression.
I.4.3 Properties of OLS Estimators.
I.4.4 Multivariate Linear Regression.
I.4.5 Autocorrelation and Heteroscedasticity.
I.4.6 Applications of Linear Regression in Finance.
I.4.7 Summary and Conclusions.
I.5 Numerical Methods in Finance.
I.5.3 Interpolation and Extrapolation.
I.5.5 Finite Difference Approximations.
I.5.6 Binomial Lattices.
I.5.7 Monte Carlo Simulation.
I.5.8 Summary and Conclusions.
I.6 Introduction to Portfolio Theory.
I.6.2 Utility Theory.
I.6.3 Portfolio Allocation.
I.6.4 Theory of Asset Pricing.
I.6.5 Risk Adjusted Performance Measures.
I.6.6 Summary and Conclusions.
Professor Alexander is one of the world’s leading authorities on market risk analysis. For further details, see www.icmacentre.rdg.ac.uk/alexander