Correlation Basics: Definitions, Applications and Terminology
Empirical Properties of Correlation: How do Correlations Behave in the Real World?
The Pearson Correlation Model – Work of the Devil?
Cointegration – A Superior Concept to Correlation?
Financial Correlation Modelling – Bottom-up Approaches
Valuing CDOs with the Gaussian Copula – What Went Wrong?
The One-Factor Gaussian Copula Model – Too Simplistic?
Financial Correlation Models – Top-Down Approaches
Stochastic Correlation Models
Quantifying Market Correlation Risk
Quantifying Credit Correlation Risk
Hedging Correlation Risk
Correlation Trading Strategies – Opportunities and Limitations
Credit Value at Risk under Basel III – Too Simplistic?
Basel III and XVAs
Fundamental Review of the Trading Book
The Future of Correlation Modelling
Answers to Questions and Problems in Correlation Risk Modelling and Management
“Behold the fool saith, ‘Put not all thine eggs in the one basket’”
– Mark Twain
In this introductory chapter, we define correlation and correlation risk, and show that correlations are critical in many areas of finance such as investments, trading, and risk management, as well as in financial crises and in financial regulation. We also show how correlation risk relates to other risks in finance such as market risk, credit risk, systemic risk, and concentration risk. Before we do, let’s see how it all started.
A SHORT HISTORY OF CORRELATION
As with many groundbreaking discoveries, there is a bit of a controversy as to who the creator of the concept of correlation is. Foundations on the behaviour of error terms were laid in 1846 by the French mathematician Auguste Bravais, who essentially derived what is today termed the “regression line”. However, Helen Walker (1929) describes Bravais nicely as “a kind of Columbus, discovering correlation without fully realising that he had done so”. Further significant theoretical and empirical work on correlation was done by Sir Walter Galton in 1886, who created a simple linear regression and interestingly also discovered the