Market Risk Analysis Volume I: Quantitative Methods in Finance

Contents

List of Figures

List of Tables

List of Examples

Foreword

Preface to Volume I

I.1 Basic Calculus for Finance

I.1.1 Introduction

I.1.2 Functions and Graphs, Equations and Roots

I.1.2.1 Linear and Quadratic Functions

I.1.2.2 Continuous and Differentiable Real-Valued Functions

I.1.2.3 Inverse Functions

I.1.2.4 The Exponential Function

I.1.2.5 The Natural Logarithm

I.1.3 Differentiation and Integration

I.1.3.1 Definitions

I.1.3.2 Rules for Differentiation

I.1.3.3 Monotonic, Concave and Convex Functions

I.1.3.4 Stationary Points and Optimization

I.1.3.5 Integration

I.1.4 Analysis of Financial Returns

I.1.4.1 Discrete and Continuous Time Notation

I.1.4.2 Portfolio Holdings and Portfolio Weights

I.1.4.3 Profit and Loss

I.1.4.4 Percentage and Log Returns

I.1.4.5 Geometric Brownian Motion

I.1.4.6 Discrete and Continuous Compounding in Discrete Time

I.1.4.7 Period Log Returns in Discrete Time

I.1.4.8 Return on a Linear Portfolio

I.1.4.9 Sources of Returns

I.1.5 Functions of Several Variables

I.1.5.1 Partial Derivatives: Function of Two Variables

I.1.5.2 Partial Derivatives: Function of Several Variables

I.1.5.3 Stationary Points

I.1.5.4 Optimization

I.1.5.5 Total Derivatives

I.1.6 Taylor Expansion

I.1.6.1 Definition and Examples

I.1.6.2 Risk Factors and their Sensitivities

I.1.6.3 Some Financial Applications of Taylor Expansion

I.1.6.4 Multivariate Taylor Expansion

I.1.7 Summary and Conclusions

I.2 Essential Linear Algebra for Finance

I.2.1 Introduction

I.2.2 Matrix Algebra and its ...