Financial Risk Modelling and Portfolio Optimization with R

9

Modelling dependence

9.1 Overview

In the previous chapters alternatives to the Gaussian model have been put forward for assessing market price risks of single financial instruments. The potential losses arising from holding a position in an asset were interpreted as a random variable and unconditional as well as conditional risk measures were derived.

In this chapter the topic of financial risk modelling in the context of multiple financial instruments is addressed. Section 2 introduces the correlation coefficient between two assets and investigates its appropriateness as a measure of dependence between two assets. Section 3 discusses alternative measures of dependence, namely the use of rank correlations and the concept of the copula. Section 7 provides a synopsis of the packages that specifically include copula modelling. Finally, Section 13 shows how copula models can be fruitfully combined with the techniques outlined in Chapters 6–8. In particular, a GARCH–copula model is proposed for measuring the market risk of a portfolio.

9.2 Correlation, dependence and distributions

The computation and usage of Pearson’s correlation coefficient is quite ubiquitous in the quantitative analysis of financial markets. However, applied quantitative researchers are often unaware of the pitfalls involved in careless application and usage of correlations as a measure of risk. It is therefore ...