Chapter 16

Advanced Risk Models: Multivariate*

We now turn to the measurement of risk across large portfolios. A risk system has three components: (1) a portfolio position system, (2) a risk factor modeling system, and (3) an aggregation system.

The first component is described in Section 16.1. Portfolio positions must be collected and then processed through mapping, which consists of replacing each instrument by its exposures on selected risk factors. Mapping considerably simplifies the risk measurement process. It would not be feasible to model all instruments individually, because there are too many. The art of risk management consists of choosing a set of limited risk factors that will adequately cover the spectrum of risks for the portfolio at hand.

The second step is to describe the joint movements in the risk factors. wo approaches are possible. The first specifies an analytical distribution, for example, a normal joint distribution. More generally, the joint movements can be characterized by copulas, which are described in Section 16.2. In a second approach, the joint distribution could be simply taken from empirical observations, without making any additional assumptions.

The third step brings together positions and risk factors. Section 16.3 describes the three main value at risk (VAR) methods, which include the delta-normal method, the historical simulation (HS) method, and the Monte Carlo simulation method. The methods are illustrated with an example in Section 16.5. ...