I'm hoping to check my understanding of this and to fill in a few gaps:
Total BEL = PV (Benefits + Expenses - Premiums)
Benefits
These include both those guaranteed to date and future discretionary benefits.
This is calculated as:
max(smoothed AS, guaranteed benefits at time of claim)
= smoothed AS + cost of guarantee
= smoothed AS + max(0 , guaranteed benefit - smoothed AS)
= (a) + (b)
So, in practice:
(a) Project the smoothed AS using expected future premiums, expenses (or charges, depending on how the AS is calculated) and the risk-free rate as the investment return
- Does this need to be done stochastically (with investment return as the stochastic variable)?
- Is this called smoothed AS because it is projected using expected investment returns (i.e. expected risk-free rate)? I would expect the comparison to be against unsmoothed AS, since smoothed AS may be higher than unsmoothed - in which case we'd be underestimating the cost..?
(b) Use a stochastic model which includes the projection in (a) and which also projects the guaranteed benefit as the current guaranteed benefit accumulating at future RB rates. The future RB rate would be an assumption (perhaps initially set to equal the current RB rate) set dynamically (i.e. linked to the risk-free rate so that it increases when the risk-free rate increases, and vice versa)
- In this case, the smoothed AS is modelled stochastically: it's calibrated so that the expected investment return is the risk-free return, with the distribution of returns around this mean set so as to mirror those of the underlying assets. Is that right
BEL for guaranteed benefits = PV (Benefits + Expenses - Premiums)
Benefits
Here we are only modelling those benefits guaranteed to date but the calculation is similar except:
(a) Smoothed AS is projected by taking the AS at the valuation date and projecting it using expect investment returns (risk-free) only - i.e. future premiums are not modelled (although future expenses relating to renewal and investment costs would be)
(b) The guaranteed benefit is known and so doesn't need to be modelled assuming future RB rates. I'm a little stuck on the rest of this calculation...?