## Risk and models under Solvency II

Insurers need to have internal models for their major risks. Indeed, both the Individual Capital Assessment (ICA) regime in the UK and the pending Solvency II rules in the EU demand that insurers have good models for their risks.

However, when building a model for mortality or any other kind of risk, you have a number of known issues in the modelling process:

1. Model risk. You do not actually know what model structure is most appropriate for your portfolio or risk.  This is particularly keenly felt for mortality projections.
2. Basis risk. Even if you have the correct model, you should be calibrating it using the same population you want to model. However, if you fit a model to the experience from one portfolio, yet use it to assess the risk in a second, you run the risk that the model is not portable.
3. Parameter risk. Even with a good data set for your portfolio and a good model to fit, your parameter estimates are still subject to uncertainty.
4. Idiosyncratic risk. Even if your model is robust as a whole, you cannot predict precisely when an individual will die.
5. Concentration risk. Linked to idiosyncratic risk, the cost of uncertainty over when an individual dies is magnified in financial significance if that person has an unusually large benefit.

Each of these risks to your modelling process is potentially measurable:

1. In the case of model risk, the obvious solution is to try a variety of models.  This doesn't eliminate model risk, but it reduces the impact of relying on one which might turn out to be wrong.
2. Basis risk is best dealt with by building and calibrating a model to the experience data of the portfolio itself. If a model is not calibrated using the portfolio's own data, say a projection model based on population statistics, then an explicit reserve will need to be held for basis risk.
3. Parameter risk can be explored by varying a parameter in a way consistent with the estimated standard error. The rest of the model can be refitted subject to this parameter being fixed, and the impact tested on the valuation of liabilities.
4. Idiosyncratic risk is best explored by simulating the entire portfolio in run-off.  This must be done on a life-by-life basis, as selecting a handful of model points to "represent" the portfolio will not help.
5. Concentration risk is also best explored by simulation, again on a life-by-life basis. A handful of model points cannot summarise the rich diversity of benefits and risk profiles in a portfolio.

In the UK the Financial Services Authority (FSA) has said repeatedly that it wants to see ICAs embedded in the management of insurers (the "use test").  Without wishing to second-guess the regulators, a life office is therefore likely to find itself under greater scrutiny the more of the following apply:

• performing ICA/Solvency II calculations infrequently
• using a single model for a risk
• using models only calibrated to population data
• using model points instead of simulating the whole portfolio
• using models without acknowledging parameter risk

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##### Run-off simulations in Longevitas

Longevitas does full portfolio run-off simulations on a life-by-life basis. The output enables the measurement of trend risk, idiosyncratic risk and concentration risk, and you can examine the variation in time lived, cash paid and the value of cashflows paid.  The risks associated with model-point selection are side-stepped by simulating every single life.

Longevitas can also perturb a nominated parameter between each portfolio simulation.  This is done with respect to the estimated standard error for the parameter concerned, with the rest of the model being fitted around the perturbed value.  This "perturbation run-off" allows the measurement of the impact of parameter risk on time lived, cash paid and the value of cashflows.