OVERVIEW

0. Preface (download)

What We're About

Contents Overview

Audience

How to Read the Book

Notation and Terminology

1. Value-at-Risk

History

Measures

Risk Measures

Market Risk

Value-at-Risk

Risk Limits

Examples

VaR Measures

ESSENTIAL MATHEMATICS

2. Mathematical Preliminaries

Notation and Terminology

Gradient and Gradient-Hessian Approximations

Ordinary Interpolation

Complex Numbers

Eigenvalues and Eigenvectors

Cholesky Factorization

Minimizing a Quadratic Polynomial

Ordinary Least Squares

Cubic Spline Interpolation

Finite Difference Approximations of Derivatives

Newton's Method

Change of Variables Formula

Numerical Integration in One Dimension

Numerical Integration in Multiple Dimensions

3. Probability (download)

Prerequisites

Parameters

Parameters of Random Vectors

Linear Polynomials of Random Vectors

Properties of Covariance Matrices

Principal Component Analysis

Uniform and Related Distributions

Normal and Related Distributions

Mixtures of Distributions

Moment-Generating Functions

Quadratic Polynomials of Joint-Normal Random Vectors

The Cornish-Fisher Expansion

Central Limit Theorem

The Inversion Theorem

Quantiles of Quadratic Polynomials of Joint-Normal Random Vectors

4. Statistics and Time Series Analysis

From Probability to Statistics

Estimation

Maximum Likelihood Estimators

Stochastic Processes

White Noise, Autoregressive and Moving Average Processes

GARCH Processes

Regime-Switching Processes

5. Monte Carlo Method

The Monte Carlo Method

Realizations of Samples

Pseudorandom Numbers

Testing Pseudorandom Number Generators

Implementing Pseudorandom Number Generators

Breaking the Curse of Dimensionality

Pseudorandom Variates

Variance Reduction

VALUE-AT-RISK

6. Market Data (download)

Forms of Data

Nonsynchronous Data

Data Errors

Data Biases

Futures

Implied Volatilities

7. Inference

Selecting Key Factors

Current Practice

Unconditional Leptokurtosis and Conditional Heteroskedasticity

Historical Realizations

8. Primary Mappings

Day Counts

Primary Mappings

Example: Equities

Example: Forwards

Example: Options

Example: Physical Commodities

9. Remappings

Holdings Remappings

Global Remappings

Change-of-Variables Remappings

Principal-Component Remappings

10. Transformations

Linear Transformation Procedures

Quadratic Transformation Procedures

Monte Carlo Transformation Procedures

Variance Reduction