Sept 2016 Q2(iii)

Because this has to be a market-consistent valuation, the stochastic investment return model has to be calibrated so that the expected return that it simulates is the risk-free rate - and this has to be the same irrespective of the type(s) of asset held. Hence the phrasing used in the Examiners' Report. But the distribution or volatility of the simulated returns around that expected return will vary according to the underlying asset type (e.g. higher volatility or spread of simulated returns for equities).

Other way around: the cost of the guarantee (i.e. the excess cost of providing the guaranteed benefit in excess of the unit fund available) is the present value of the guaranteed annuity less the unit fund value. The guarantee would only be taken if the guaranteed annuity rate is greater than the market annuity rate available at that date, so the model needs to compare the guaranteed annuity rate with the simulated annuity rate. If the simulated annuity rate is higher, then the policyholder would not take the guarantee and the guarantee has no value. Hence the Examiners' Report solution starts from the annuity rate comparison. The present value of the market annuity that could be purchased will equal the unit fund value, so it boils down to the same thing as {PV guaranteed annuity - unit fund value}, if this is greater than zero and guaranteed annuity rate > simulated market annuity rate.

Yes: but it is effectively included for those policies that are assumed to exercise the GAO, since the cost of guarantee element includes the present value of the guaranteed annuity benefit.

 

I think the confusion might arise because the ER is working in terms of annuity rates (a fraction or % applied to the fund value in order to determine the absolute amount of annuity benefit which will be paid each period) rather than annuity amounts. We also need to make use of annuity valuation factors: the "little a" annuity factors that were introduced in the CT subjects, in order to provide the total cost of the annuity payable throughout the lifetime.

For example, in your first bullet point above, the first line could be written as "where the guaranteed benefit would be calculated as the guaranteed fixed annuity multiplied by an annuity valuation factor, where the latter is based on the interest rates and mortality expected at the time at which the guarantee is exercised."

The total cost or value of the annuity = annuity amount x annuity valuation factor = unit fund x annuity rate x annuity valuation factor.

So the cost of the guarantee can be calculated as: unit fund value x max {0, guaranteed annuity rate - simulated market annuity rate} x annuity valuation factor.

The ER has combined the latter two components of this calculation into max {0, annuity valuation factor x {guaranteed annuity rate - simulated market annuity rate}}, calling the latter component "the present value of an annuity based on {guaranteed annuity rate - simulated market annuity rate}".

Hope that helps.

 

Hello

Same principles would apply: average value across simulations of max [PV of guaranteed benefit - PV of benefit otherwise payable, 0].

A non-linked product with GAO would be a WP policy. So for example we'd use the projected maturity value of the WP policy rather than the unit fund used in for the UL policy in this question.