Correlation Risk Modelling and Management (2nd Edition)
First published:
ISBN: 978-1-78272-405-6
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Stochastic Correlation Models
Stochastic Correlation Models
Introduction
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
“I think correlation modelling is basically at the stage volatility modelling was about 15 years ago”
– Vladimir Piterbarg
In finance, many variables such as equities, bonds, commodities, exchange rates, interest rates and volatility are often modelled with a stochastic process. In addition, from our empirical Chapter 2, we derived that financial correlations behave somewhat erratic and random. Therefore, it seems like a good idea to model financial correlations with a stochastic process.
The modelling of financial correlation with a stochastic process is fairly new, but several promising approaches exist. We will discuss them, but, before we do, let’s look at some basics.
WHAT IS A STOCHASTIC PROCESS?
The reader who has made it all the way to this chapter has, hopefully, a good idea of what a stochastic process is. But let us have a closer look. Let’s start with a deterministic process. A deterministic process is a process with a known outcome. For example counting numbers by one and the movement of the sun are deterministic processes. The opposite of a deterministic process is a stochastic process, also called “random process”. Hence, heuristically (meaning non
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