Credit Risk in Loan Portfolios

Alexander Denev

The previous chapter described the application of PGMs to the problem of how to optimally determine the asset side of a firm with an investment mandate. We also showed a case study of liability-driven investment (LDI) by including in the optimisation the liability side for either an insurer or a pension fund. In this chapter we show how to use PGMs to assess the tail risk of a portfolio of assets that are not marked-to-market but nevertheless subject to default risk.

The asset composition of banks is divided into banking and trading books¹¹ An asset can be switched between the two books over the course of its life. The trading book includes supposedly tradeable and liquid instruments (eg, bonds, derivatives) and must to be marked-to-market. The banking book comprises assets that are meant to be held to maturity. For example, it includes loans made to third parties. This is usually the core business of a commercial bank and one for which there is a negligible liquid secondary market. The risk measures for the two books are different in the Basel rules: VaR for the trading book and RWA for the banking book (we discussed these in Chapter 1).²² Recall that the VaR for assets in the