In the case of a single reference instrument, the risky position can be discounted with that instrument. Monetary risk measures are then applied to the discounted position.
However, in the situation of several reference instruments, it is not possible to discount the risky position because we do not know which of the reference instruments should be used for discounting. For example, if the financial operator has the possibility to invest the money in a bank account and in various zero-coupon bonds, simple discounting with the bank account is only an approximation of the actual capital requirement. The use of so-called multi-asset risk measures is not subject to this disadvantage.
We therefore consider multi-asset risk measures in common market models, such as the Black-Scholes model. Due to the current phase of low interest rates, special attention is also paid to models with stochastic interest rate developments. In order to create risk measures that are competitive with monetary risk measures, a key task is to consider realistic trading opportunities in relation to the reference instruments.
The results found are applied to extreme loss developments in the general insurance sector. This requires the use of methods from extreme value theory. The main question is how robust our risk estimation is.
Goals of the Project
Finally, we briefly summarise the project objectives described above:
- Finding realistic trading opportunities with reference instruments
- Determination of the change in capital requirements by using multi-asset risk measures
- Analysis of the effects of extreme events on the coverage of risks