Loss portfolio transfer treaties within Solvency II capital system: a reinsurer’s point of view

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Loss portfolio transfer (LPT) is a reinsurance treaty in which an insurer cedes the policies that have already incurred losses to a reinsurer. This operation can be carried out by an insurance company in order to reduce reserving risk and consequently reduce its capital requirement calculated, according to Solvency II. From the viewpoint of the reinsurance company, being a very complex operation, importance must be given to the methodology used to determine the price of the treaty.
Following the collective risk approach, the paper examines the risk profiles and the reinsurance pricing of LPT treaties, taking into account the insurance capital requirements established by European law. For this purpose, it is essential to calculate the capital need for the risk deriving from the LPT transaction. In the case analyzed, this requirement is calculated under Solvency II legislation, considering the measure of variability determined via simulation. This quantification was also carried out for different levels of the cost of capital rate, providing a range of possible loadings to be applied to the premium.
In the case of the Cost of Capital (CoC) approach, the results obtained provide a lower level of premium compared to the percentile-based method with a range between 2.69% and 1.88%. Besides, the CoC approach also provides the advantage of having an explicit parameter, the CoC rate whose specific level can be chosen by the reinsurance company based on the risk appetite.

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    • Figure 1. Probability density function of current random value of future compensation for the whole of generation Z
    • Figure 2. Cumulative distribution function of generation Z
    • Table 1. Base scenario: hypothesis
    • Table 2. Statistics on the current value of compensation
    • Table 3. Cumulative distribution function of generation Z – F(z)
    • Table 4. Coefficient of Variation (CoV) of BEL (Best Estimate Liabilities)
    • Table 5. BEL and 95th percentile
    • Table 6. Premium with CoC approach
    • Table 7. Parameters in the scenarios
    • Table 8. Sensitivity analysis on investment risk and insurance risk
    • Conceptualization
      Nicolino Ettore D’Ortona, Gabriella Marcarelli, Giuseppe Melisi
    • Methodology
      Nicolino Ettore D’Ortona, Gabriella Marcarelli, Giuseppe Melisi
    • Software
      Nicolino Ettore D’Ortona
    • Supervision
      Nicolino Ettore D’Ortona
    • Writing – original draft
      Nicolino Ettore D’Ortona
    • Investigation
      Gabriella Marcarelli, Giuseppe Melisi
    • Writing – review & editing
      Gabriella Marcarelli, Giuseppe Melisi
    • Data curation
      Giuseppe Melisi