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
“If you can’t explain it in simple terms, you haven’t understood it very well”
– Albert Einstein
In the previous chapter we looked at the numerous limitations of the Pearson correlation model. In this chapter we discuss the concept of cointegration and evaluate if it is a better suited concept to analyse financial time series and their dependence.
Cointegration is a 2003 Nobel Prize-rewarded concept and goes back to Robert Engle and Clive Granger (1987). Before we analyse it, we have to understand some statistical properties, which are part of Cointegration.
What is a stationary process?
Definition: A stationary process is a process where mean and variance are constant in time (weak stationary) or all moments (strict stationary) are constant in time.
An example of a stationary process is a random drawing from a standard normal distribution εt, which we already encountered in Chapter 3. ε can be computed as =normsinv(rand()) in Excel or norminv(rand) in MATLAB. See www.dersoft.com/epsilon.xlsx for a spreadsheet deriving ε. Drawing 10,000 εt, we derive Figure 4.1.
However, stocks that grow are not stationary, since their mean increases in time. In