1) Yes, an insurer would normally take lapse rates into account in their pricing basis - which tends to be a best estimate basis.
Regarding lapse rates and mortality rates, consider 'selective withdrawals' on say protection policies, where those who withdraw tend to be the healthier lives, so the insurer is left with more unhealthy lives, ie with a higher mortality.
2) Normally yes, but this will depend on whether the reserve is on a prudent or more of a best estimate basis. If prudent, the insurer would then need to consider if higher or lower withdrawals are more prudent. If lower withdrawals are, then it could be argued that they shouldn't be included. However under SII, where the basis is best estimate, they would be included.
Thanks
Em
Thank you very much for your response.
Regarding incorporating lapse rate into the pricing procedure.
I would like to take an example to illustrate my concern:
For example, we are to calculate the net premium for an insurance product using the equivalence principle that:
- Pays K if the insured dies within T years
- If the insured "lapse" (or say, "surrender") at time t before maturity, he will receive the policy value at t (i.e. V(t))
To price this product, we have the equation:
Expectation[Discounted future premium] = Expectation[Discounted future benefit]
where future benefit includes 2 parts: K if dies and V(t) if surrender.
However, we know that V(t) is a function of Future premium and Future benefit after time t (discounted to t).
And the future benefit again includes 2 parts: K if dies and V(t') if surrender. And V(t'), again, is a function of future premium and future benefit (after time t')
And on and on.
So basically, the recursive relationship of policy value V(t) makes the calculation very complicated. And I don't know how to overcome it.
Could you please explain me:
- How to deal with this kind of problem when we want to pricing a product that include the lapse opportunity for the client ?
- In practice, do people directly incorporate the lapse into the pricing problem like this or they will do differently ?
Thank you very much for your help!