Chapter 15
Advanced Risk Models: Univariate*
We now turn to more advanced risk models. First, we consider univariate risk models. Multivariate models are presented in the next chapter.
This chapter covers improvements to traditional risk models. In practice, the implementation of risk models for large institutions involves many shortcuts, simplifications, and judgment calls. The role of the risk manager is to design a system that provides a reasonable approximation to the risk of the portfolio with acceptable speed and cost. The question is how to judge whether accuracy is reasonable.
This is why risk models must always be complemented by a backtesting procedure. This involves systematically comparing the risk forecast with the subsequent outcome. The framework for backtesting is presented in Section 15.1.
Next, we examine a method to improve the estimation of the tail quantile beyond the traditional historical-simulation and delta-normal methods, which can be defined as nonparametric and parametric, respectively. Section 15.2 turns to extreme value theory (EVT), which can be used to fit an analytical distribution to the left tail. This method, which can be described as nonparametric, gives more precise value at risk (VAR) estimates. In addition, the analytical function can be used to extrapolate VAR to other confidence levels.
Finally, Section 15.3 considers properties for risk measure. A risk measure that satisfies the selected properties is called coherent. It shows that, in ...
