Hello all, I am confusing a little bit about the lapse rate. I have 2 questions: 1. When we do the pricing of a new insurance product, do we take into account the lapse rate or not? Does the lapse rate have any effect on the mortality rate? 2. Do we take into account the lapse rate when we calculate reserve? Why do we have to do so ? Thank you all for your help!
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!
Hi I would recommend revisiting your CM1 notes. If a cashflow approach is used then these withdrawals can easily be incorporated. And yes as you have alluded to, this could be an iterative process: For a conventional insurance products, the sum assured will be set, ie K in your example. The surrender terms are also likely to be set separately, following surrender value principles (as set out in SP2). In the profit testing model, multiple decrements for death and withdrawals (eg (aq)w/x dependent probabilities of leaving the population due to withdrawals at age x and (aq)d/x dependent probabilities of leaving the population due to death at age x) would likely be used. With predetermined discontinuance terms V(t) applied to the (aq)w/x and predetermined K's applied to (aq)d/x. This would work out the profit signatures, which would need to be discounted to work out the net present value. We would then need to compare to the profit criterion. If this is not met, a decision would then be made as to whether the premiums and/or discontinuance terms would need to be changed. When I was in industry we used to use such methods in our cashflow projections, with surrender terms varying by policy inforce. However, I will leave it to anyone else to confirm what happens now. Hope this helps. Thanks Em
