August 23rd, 2010

QIS5 – Premium and Reserve Risk: Sufficient Consideration of Non-proportional Reinsurance?

Posted at 1:00 AM ET

Frank Achtert, Managing Director, Financial Intelligence Team, and Sebastien Portmann, Vice President, Financial Intelligence Team

On July 6, 2010 the Committee of European Insurance and Occupational Pensions Supervisors (CEIOPS) published the technical specification for the latest Solvency II Quantitative Impact Study (QIS) 5. QIS5 is scheduled to be carried out from August to November of 2010, with a report summarizing the results scheduled for release in April of 2011. Regarding the non-life premium and reserve and risk, Guy Carpenter & Company, LLC has observed a return to capital requirements more in line with QIS4 and an implicit incentive for the use of an internal model.


Following the recent global financial crisis, CEIOPS intended to dramatically increase the risk factors for underwriting risk (see Consultation Paper 71 and Final Advice). Pressure and lobbying efforts from the industry seem to have been successful, as shown by the fact that the premium and reserve risk factors to be used for the QIS5 exercise are definitely more in line with - but on average slightly above - 2008’s QIS4 levels:


The factors represent market-wide estimates of the standard deviations for premium and reserve risk.

Reflection of non-proportional reinsurance

The good news is that for the first time risk carriers have the option of adjusting the premium risk factor per line of business according to their non-proportional reinsurance structure in place. The goal of the newly introduced adjustment factor “NP” is to tailor the capital requirement through a more accurate recognition of the effect of non-proportional reinsurance on the overall claims volatility. In practice, the NP-factor can take values between 0 and 1 and is multiplied with the underwriting risk factor to get the net risk factor. To calculate the company specific adjustment factor, carriers have to parameterize, for each line of business, a lognormal distribution for the gross cost per claim based on historical data. Retentions and limits of the non-proportional covers in place are then factored into the calculation. Only per risk excess of loss reinsurance contracts which allow for reinstatements can be taken into account.

Although the introduction of the factor is a major improvement in the effort to reflect non-proportional reinsurance in the Solvency II standard formula, it suffers some technical and practical drawbacks:

  • For a line of business, the NP-factor may not be stable over time, even with a large number of observed losses. In particular the occurrence of a larger than usual claim will affect the factor dramatically.
  • The use of lognormal function to fit the historical losses may be of questionable appropriateness.
  • It is unclear whether historical losses have to be developed and adjusted for inflation, which can clearly distort the final outcome.
  • The computation of the NP-factor requires a huge amount of data that may not be readily available.
  • The NP-factor can be estimated for standard excess of loss treaties allowing for reinstatements only; no stop loss, or special features like aggregate annual limit or deductible.


Insurers willing to adjust the underwriting risk factor by means of the NP-factor should evaluate whether a (partial) internal model would not be the more appropriate solution. Provided the number of historical observations is sufficient and over a long enough period, a partial internal model component can indeed be constructed using the same data basis as the one required for the derivation of the NP-factor. In such a case, most, if not all, drawbacks of the NP-factors described above are overcome.

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