Development of a capital market model


The aim is to develop a stochastic capital market model for application to asset-liability management and other applications in insurance companies and pension liabilities.
The model should do justice to its task and objective as far as possible, but without becoming too complex, according to the rule of thumb: “As simple as possible, as complicated as necessary”. The more complex the model, the more time and effort is needed to calibrate and adjust it, while the additional gain in knowledge decreases.


Among stochastic models, one can roughly distinguish two families:

  • Econometric models (“Real World”), as they are applied in risk models, ALM models, collective models. Here, we understand risk models to be those fat-tail models that estimate not only the amplitude of the event (amount of damage) but also its probability.
  • Arbitrage-free models (“Risk-Neutral”), which are indispensable for valuation models of structures and derivatives, and are suitable for optimisations of asset allocation.

In addition, there are of course also the deterministic single-scenario models, which find application especially in stress tests for estimating the amplitude of the event with very simplistic probability estimation. The best-known example of this is Solvency II.

Other criteria to be considered in addition:

  • Time horizon (e.g. 5-10 years for life, 1-3 years for non-life, 10-30 years for pensions)
  • One- or multi-period time steps (e.g. quarterly or annual steps)
  • Number of scenario paths (e.g. for optimisations rather less, for valuations rather more)
  • Use of economic regimes with correspondingly different parameter sets
  • Anfluss on accounting, e.g. through credit migrations, impairments, book vs. market value considerations
  • Different currency areas, esp. if there is no currency mismatch

We also distinguish in the modelling of variables and their interrelationships:

  • fundamental modelling (e.g. credit as a combination of bonds and equities),
  • regression-based modelling, respectively based on the moments and covariances of the historical distributions.

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