R Programming for Actuarial Science

13 Copulas

Peter McQuire

library (MASS)
library (copula)

13.1 Introduction

In many financial and actuarial settings, the modelling of multivariate distributions will form a crucial part in analysing the aggregated risks to which a financial institution is exposed. For example, an insurer will be interested in the incurred claims under each individual class or type of insurance it writes; however, of greater importance is the combined total claims amount from all its classes of business in a single time period. Crucially, the level of correlation between policies may vary substantially, often depending on varying economic conditions; insurer insolvency may occur if high claim levels from all insurance classes coincide at the same time. Similarly, a banking regulator will be interested in understanding the likelihood of a number of banks failing over a short period of time, and it may well be that losses in the banking sector are particularly highly correlated during periods of stressed financial conditions. To develop the best models we must aim to capture both the degree and the pattern of any dependencies which exist in our data. Copulas can help us do this.

The use of copulas in the financial sector has grown significantly since David Li published his paper in 2000, “On Default Correlation: A Copula Function Approach”, in which he described how the Gaussian copula can be used to help in the pricing of collateralized debt obligations (CDOs). However their application was ...