May I know the formula for the COG as calculated in pillar 1 peak 2? This comes under future policy related Liab. The core reading mentioned that if the annual bonus declared is higher than the assumed bonus used in the calculation of FPRL, COG will increase. May I know why?
The cost of guarantee is too complicated to show as a simple formula. You would need to use stochastic simulations to incorporate management actions in practice. However, an approximation that gets the right sort of idea is the Black-Scholes equation for a put option. We want to work out the cost of the guarantee biting, ie the sum assured and reversionary bonuses being bigger than the asset share (if we calculate the WPBR retrospectively). So the share price in the B-S formula is the current asset share and the exercise price is the sum assured plus reversionary bonuses. Now, when we worked out the FPRL last year, we would have assumed a certain rate of bonus to get the reversionary bonuses at maturity in the B-S formula above. If the actual bonuses over the year were larger than this, then our new reversionary bonuses as projected at the end of the year will be bigger, the exercise price for the B-S formula has gone up, and COG has increased. I hope this helps. Mark
In the Sept 09 paper, Question 2 (iii) (c), where the question is about the effect of increased FI yields on the Pillar 1 Peak 2 working capital, the examiner's report says: "But the reduction in cost of guarantees may be offset to some extent if regular bonus rates are assumed to increase." I thought like you said, the cost of guarantees compare the projected AS with the guaranteed benefits (SA + any declared bonuses). But the answer seems to imply that future regular bonuses are also taken into account?
Thanks for asking for clarification. I'm sorry if this was not clear before. Yes, future regular bonuses are taken into account in the FPRL. We are comparing the asset share to the guarantees at maturity. As I said in the earlier thread "when we worked out the FPRL last year, we would have assumed a certain rate of bonus to get the reversionary bonuses at maturity in the B-S formula". Best wishes Mark
