Portfolio modelling of counterparty reinsurance default risk

Modelling counterparty default risk of a reinsurance bouquet requires an appropriate underlying default correlation structure. A flexible model with two control parameters gives us an alternative of the current standard model in Solvency II

We treat the bouquet of reinsurance treaties and the induced counterparty default risk for a primary insurer as similar to an investment portfolio. Contrary to traditional mean-variance portfolio design, which implies a large number of realisations of random variables and comparable sized components, reinsurance default risk typically is a rare event process with potential large severity components. Moreover, the covariance structure is largely driven by a common shock. The probability law for this common shock, as well as the vulnerability of insurance companies to this shock, guide the derivation of the various key-quantities necessary for the determination of the solvency capital requirement.

The new risk-based solvency and supervisory standard for European (re)insurance companies, Solvency II, is planned to be introduced in 2012. In the process of completing it, insurance supervisors in Europe are developing and testing a set of risk modules together spanning the standard model in Solvency II for the calculation of the solvency capital requirement (SCR). Since this set of modules is expected to cover "all risks", not only traditional risk categories like market risk and underwriting risks are covered, but also more specialised risk categories. One of the more esoteric modules targets counterparty default risk, which focuses on the default risk of reinsurance and other risk mitigating instruments.

1. Conditionally on the shock size the true probability distribution follows from convolution of the various independent risks, which are modelled as two-point distributions. Weighting these conditional (discrete) distributions with the (discretised) probability of shock-size gives the true probability distribution. It will have a firm probability mass at zero followed by a bumpy tail to the right. For Solvency II purposes such an approach seems a bridge too far. For internal models this might be a valid route.

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REFERENCES

Proposal for a Directive of the European Parliament and of the Council on the taking-up and pursuit of the business of Insurance and Reinsurance,

Solvency II, Brussels 10.7.2007

QIS3 Technical Specifications Part I: Instructions,

CEIOPS-FS-11/07 April 2007.