Dynamic copula methods in finance

Umberto Cherubini, Fabio Gobbi, Sabrina Mulinacci and Silvia Romagnoli

Over the course of the past decade financial markets have witnessed a marked increase in the use of correlation dynamics models - new terms such as correlation trading and correlation products have now become mainstream, and, increasingly, trading and investment activities have involved more and more exposure to credit risks that are non-Gaussian by definition. By addressing the restrictions which must be imposed on copula functions to yield dynamically consistent results this book sets out the latest research into the application of copula functions to the solution of financial problems.

Beginning with a review of the issues surrounding dependence and correlation in finance and the basic concepts of copulas as they have been applied to financial problems up until now, the book goes on to introduce the theory of convolution-based copulas, and the concept of C-convolution within the mainstream of the Darsow, Nguyen and Olsen (DNO) application of copulas to Markov processes. The authors explain how the C-convolution approach can be exploited to address both spatial and temporal dependence - a twofold perspective which is entirely new to these applications - and demonstrate how it can be applied to the problems of evaluating multivariate equity derivatives, analyzing the credit risk exposure of a portfolio, and aggregating Value-at-Risk measures across risk-factors and business units.

It shows the reader how to build original and consistent copula-based solutions to problems such as:

• The evaluation of multivariate and path dependent equity linked derivatives consistent with the no-arbitrage requirement imposed by financial theory and the "fair value" principle
• The evaluation of multivariate credit derivatives with a focus on the price consistency of contracts of different maturities
• A consistent strategy for aggregation and allocation of risk capital across different risk factors and business units
• A new copula-based approach to the performance analysis of mutual funds and hedge funds

The culmination of five years original research at the University of Bologna on the use of copulas in finance, this book is essential reading for practitioners involved in pricing and risk management.