# Does Solvency II demand stochastic models?

Solvency II is a major overhaul of the reserving rules for insurers throughout the European Union. An important consideration for annuity writers is how it will relate to longevity trend risk. For example, consider the following text about "Statistical quality standards" as they refer to insurers' internal models:

The methods used to calculate the probability distribution forecast shall be based on adequate, applicable and relevant actuarial and statistical techniques and shall be consistent with the methods used to calculate technical provisions. The methods used to calculate the probability distribution forecast shall be based upon current and credible information and realistic assumptions.

Source: Article 119, Commission of the European Communities (2008) "

Proposal for a Directive of the European Parliament and of the Council of 26 February 2008 on the taking-up and pursuit of the business of Insurance and Reinsurance --- Solvency II (recast)"

A literal interpretation of this is that Solvency II would expect any internal model for longevity trend risk to be a stochastic projection model. But would this be the prevailing interpretation in practice? We sought the opinions of longevity actuaries in some UK life offices with large annuity portfolios. Their responses were as follows:

In a word, yes. For practical purposes, though, careful thought is needed as to how this will be implemented, which of course depends on the overall internal model design.

[A] stochastic projection model certainly fits the description, but I wouldn't assume that it is the only approach.

I would read this as saying that if you're going to use a stochastic model , it has got to be a good one using sensible assumptions [...] I think there is an onus on firms to demonstrate why a non-stochastic model is appropriate.

For longevity, there's clearly an argument that the interaction with interest rate risk is sufficient to require a stochastic approach.

I don't share your interpretation [...] because of the expert judgement involved for insurance risk [...] in this case, firms may have to justify that [...] the model is not simply a black box, but that they understand how it works, how the inputs drive the outputs and actually use it in running the business.

In other words, there are as many opinions as there are actuaries! Whilst it seems likely that most offices will eventually use stochastic models in some form, the above quotations suggest that not every life office will start out that way.

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