Copula functions represent a methodology which has recently become the most significant new tool to handle in a flexible way the co-movement between markets, risk factors and other relevant variables which are studied in finance. It has become increasingly popular both among academics and practitioners in the field of finance principally because of the huge increase of volatility and erratic behaviour of financial markets. In this workshop we introduce the use of copulas and consider applications to diverse financial models.

Financial risk management confronts us with a real world of prices and losses which have statistical distribution with heavy-tails. Rapid changes and complex interdependencies force us to go beyond standard statistical models and simplifying assumptions of normality to develop more sophisticated methodologies which capture downside risk.

Extreme value theory (EVT) is a practical and useful tool for modelling and quantifying risk. This workshop provides an overview of the role of EVT in risk management, as a method for modelling and measuring extreme(downside) risks.

This truly comprehensive one-day workshop provides you with the most important aspects in this field. This workshop

• Introduces and delves deeply into the theoretical aspects;
• Presents the applications of copulas on market and credit risk;
• Gives you an outlook on the future development of the application of Copulas in finance; and
• Allows you to understand the practical applications of copulas in financial risk management.

Duration:
One day course

Presenters:

CARISMA Team(G Mitra, D Roman, C Fabian)
Kjersti Aas, Assistant Research Director, Norwegian Computing Center

PROGRAMME to date

Copulas: An Introduction
Kjersti Aas, Assistant Research Director, Norwegian Computing Center

Understanding and quantifying dependence is at the core of all modelling efforts in financial econometrics. The linear correlation coefficient, which is the far most used measure to test dependence,  is only a measure of linear dependence.This means that it is a meaningful measure of dependence if asset returns are well represented by an elliptical distribution. Outside the world of elliptical distributions, however, using the linear correlation coefficient as a measure of dependence may lead to misleading conclusions. Hence,alternative methods for capturing co-dependency should be considered. One class of alternatives are copula-based dependence measures. In this talk we give an introduction to copulas. We first give the formal definition of a copula, and give some examples of commonly used copulas. Further we treat the problem of estimating the parameters of a copula, and finally we present algorithms for simulating from these copulas.

A Computational Study on Portfolio Choice Models and Scenario Generation Methods
Csaba Fabian, Gautam Mitra, Diana Roman, Victor Zverovich, Tibor Vajnai, CARISMA/Brunel University

The main aim of this study is to test whether the performance of portfolio choice models is improved by using scenario generators for the future returns of the assets involved. We use two portfolio choice models, both based on Second-order Stochastic Dominance. One is the multi-objective model of Roman, Darby-Dowman and Mitra (2006) that we call unscaled model. The other is the scaled model of Fabian, Mitra, Roman and Zverovich (2010).  We construct optimal portfolios using representations of the future asset returns given by
(a) historical data,
(b) scenarios generated by Geometric Brownian Motion, and
(c) scenarios generated using Copulas.

Our test data consist of weekly returns of 68 stocks from the FTSE 100 basket, together with the weekly returns of the FTSE 100 index. We consider the period 1993-2009. Part of the data are reserved for out-of-sample tests. In both portfolio choice models, the objective is to construct a portfolio that dominates the stock to the greatest possible extent. We compare the return distributions of the respective optimal portfolios of the models.

Pair-Copula Construnctions: Even More Flexible Than Copulas
Kjersti Aas, Assistant Research Director, Norwegian Computing Center

In this talk we show how multivariate data, which exhibit complex patterns of dependence in the tails, can be modelled using a cascade of pair-copulae, acting on two variables at a time. We use the pair-copula decomposition of a general multivariate distribution and propose a
method for performing inference. The model construction is hierarchical in nature, the various levels corresponding to the incorporation of more variables in the conditioning sets, using pair-copulae as simple building blocks. Pair-copula decomposed models also represent a very flexible way to construct higher-dimensional copulae. We apply the methodology to a financial data set.