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
“Solving the right problem numerically beats solving the wrong problem analytically every time”
– Richard Martin
In this chapter, we will discuss new developments and financial modelling, which can be extended to correlation modelling. We will address the application of GPUs (graphical processing units), which allow fast parallel execution of numerically intensive code without the need of mathematical solvency. We will also discuss some new artificial-intelligence approaches such as neural networks and genetic algorithms, as well as fuzzy logic, Bayesian mathematics and chaos theory.
NUMERICAL FINANCE: SOLVING FINANCIAL PROBLEMS NUMERICALLY WITH THE HELP OF GPUS
Some problems in finance are quite complex so that a closed-form solution is not available. For example, path-dependent options such as American-style options principally have to be evaluated on a binomial or multi-nominal tree, since we have to check at each node of the tree if early exercise is rational. In risk management, especially in credit risk management, thousands of correlated default risks have to be evaluated. While there are simple approximate measures to model counterparty risk in a portfolio such