In this second market risk chapter we focus on a few important advanced topics in market risk analysis.
First, we consider an arbitrary set of portfolio profit-and-loss samples for which we wish to apply risk measures. The empirical portfolio loss distribution can come from any underlying model and the focus is hence on general simulation-based risk measures.
Second, we analyze the univariate and multivariate stylized facts of financial time series and discuss risk factor models that can capture these stylized facts. As we have mentioned before the multivariate normal distribution assumption for market risk factors is in general a simplifying assumption rather than an empirically vetted assumption. We show that models that do not capture the stylized facts tend to underestimate risk, sometimes severely. They may also fail to account for the fact that portfolio losses from one day to another can be correlated.
The third topic in this chapter is concerned with measurement horizons for market risk. In practice, financial institutions measure market risks on relatively short-term horizons such as a day. However, for regulatory reporting and other purposes, longer horizon market risk measures are also needed. We therefore discuss the concept of scaling risk measures as well as temporal aggregation of data to obtain longer horizon risk analysis. ...