A pricing technique to calculate the solvency capital requirement for non-life premium risk

The birth of Solvency II has pushed insurance Companies to build their own models in order to represent consistently their risk profiles. If the focus is on the non-life Premium Risk model, the perception is a lack of connection with actuarial best practices of pricing. The Premium Risk results from fluctuation in timing of frequency and severity, of insured events, which ensure that the premiums income will be not enough to pay future claims. Since the level of the premiums income is based on actuarial techniques of pricing, which define the risk level of each profile in portfolio, it is clear that a coherent model, used to define the Premium Risk SCR, should be based on these best practices. Further points of attention must be the CARD system and the business strategy of the Company. The actuarial department used to build GLM to define the expected frequency and severity for each claim types defined by the CARD system and for each possible combination of policyholder characteristics. Using these results it’s possible to estimate the future expected frequency and severity if their overall levels will be not change. The model developed considers all these aspects and helps the Company Board to take decisions, answering to the following fundamental question: “What will happen in terms of expected profitability, loss ratio, SCR, size of portfolio if ….?” The milestones are the policies in force on an established date. This portfolio is projected, on the time horizon referred to the calculation of the SCR, considering new business, renewal process, ageing of policyholders, bonus-malus class changing and every features that could modify the risk itself. The projected portfolio expected frequencies are estimated for each profile and for each claim types using the GLM-technique results, and are corrected to consider external factors that could change their overall levels. Meanwhile even the severity parameters are estimated analyzing the past experience.Once estimated these parameters a simulation model is built using the risk theory collective approach in order to calculate possible outcomes of the total claims amount. The main hypothesis concern the distributions used to model the cost of each claim types, both attritional and large, and the non-correlation between the claim types themselves.Once simulated the total claim cost, the Value at Risk at 99.5% and the Tail Value at Risk at 99%have been calculated and compared with both the expected total claims amount and the future expected Pure Premiums Income. In addition even the expected claims amount and the expected Pure Premiums income are compared in order to clarify the expected profitability of the tariffs in force. To calculate the real premiums income of the portfolio and the connected pure premiums the company tariffs are applied to the future portfolio and even the discount policy of the Company is taken into account in order to have a real situation.Being the main aim of that job building an useful instrument for the company board to compare future scenarios depending on their choices, the last part of the paper is focused on comparing different outcomes of the model depending on underwriting and discount policies and market scenarios.Finally the Solvency II standard formulas are applied in order to underline their main lacks and to be compared with the internal model results.