Application of multi-asset risk measures

In the financial sector, the determination of capital reserves is a common topic. These should provide protection against future risks. We use current research findings to make the determination of such capital requirements more realistic.

Banks and insurance companies are required to create capital reserves to cover future risks. By default, the determination of such reserves is based on monetary risk measures, such as value-at-risk or expected shortfall. Such risk measures are based on the assumption that the reserves are invested in a single suitable reference instrument. We deal with the question of how the capital requirement changes if not only a single but several reference instruments are available.


As an example, an insurer can hedge against the risks arising from its business activities by building up a counter position in the financial market. This may consist of bonds, shares, derivatives or other traded securities. The individual components of the portfolio in this example are the reference instruments mentioned:

Illustration der Absicherung von Risiken
© Fraunhofer ITWM
Illustration der Absicherung von Risiken

Disscounting Issues

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.

Market Models

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.


Extreme Damages

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