R Programming for Actuarial Science

15 Bond Portfolio Valuation: A Simple Credit Risk Model

Peter McQuire

15.1 Introduction

library(copula);library(lifecontingencies)

Several chapters in this book have discussed the importance of incorporating correlations in the models we have introduced. In Chapter 13 we introduced the concept of copulas which provides considerable flexibility in modelling multivariate distributions. In this chapter our objective is to model the distribution of the future value of bond portfolios; an important facet of this model is to incorporate correlations between the prices, and in particular the credit risk, of individual bonds. To do this we will make use of the Gaussian copula.

The model described in this chapter has some similarities with the Credit Metrics model which was introduced by JP Morgan in 1997, although the JP Morgan paper does not explicitly describe the Gaussian copula.

Our model uses bond ratings as a key variable in the valuation of bonds. Bonds are rated by many ratings agencies, such as Moody’s and S&P, who analyse the likelihood that each bond will default on payments over the next year. For example a Aaa rating used by Moody’s implies the bond is ‘judged to be of the highest quality, and is subject to the lowest level of credit risk’. The issuing company (or country) is considered to be extremely strong, and unlikely to default in the next year. Compare a Ca rated bond, defined to be ‘highly speculative and is likely in, or very near to, default, with some prospect ...