International School

A most important task for the risk control group of a bank is to "translate" senior management's risk appetite into absolute constraints on positions created by the traders on the floor. The directive from senior management might be "The bank can suffer a loss exceeding 3 MSEK at most once a month, and a loss exceeding 10 MSEK at most once a year". On the other hand, in the communication with the trading it is much better to present scenario based directives such as "The portfolio loss must not exceed 3 MSEK in case the short interest rate increases by 0.1%, and it must not exceed 10 MSEK in case the short rate increases by 0.5%". Therefore, when setting limits on the trading operation one is faced with the difficult problem of attaching probabilities to different market scenarios. We open this talk by reviewing how univariate extreme value theory can be used to estimate the probability of tail events for single risk factors. The probability of multivariate scenarios are extremely hard to estimate, since it is well known that in times of market stress the dependence structure of the risk factors can change drastically. We will discuss different dependence concepts, such as copulas, that can be useful in the modelling of the joint distribution of the risk factors. We will in the talk concentrate on thumb rules and easy-to-implement solutions rather than on rigorous theoretical results.