Good day I would like to inquire about the costing of investment guarantees. I understand there are two methods: (1) Options Pricing and (2) Stochastic Simulation. Unit-linked business Say we have a unit linked endowment assurance. This policy is subject to a guaranteed sum assured. Now we want to allow for the cost of such a guarantee in the premium. I understand that it can be done under method (1) by using an American Put option. But how should it be done under method (2)? In general I believe we follow: (1) Project the fund values -> (2) Run multiple simulations -> (3) Compare the fund value to the guarantee at the time of claim -> (4) Cost of guarantee is equal to the probability of guarantee biting*Average loss if it does bite; where probability of biting will simply be the number of simulations where the fund value falls short -> (5) Discount this cost of guarantee and then include it in the premium. However, with the endowment assurance, the claim could occur at any time. Say the benefit is payable at the end of the year. Then do we calculate the cost of the guarantee as described above at the end of each year and then discount all of these values to include in the premium? Additionally then can this method be used for any guaranteed surrender values as well? (Since surrender values can also be paid at any time) Or how else do we value the guaranteed surrender values? Thanks in advance!
Hi Thanks for having a go at suggesting a possible approach to valuing this guarantee. First of all it is important to note that when pricing a unit-linked policy the insurer is trying to set the charges rather than the premium. The policyholder normally decides the premium that they want to invest. Yes, we could use method (1) to value a maturity guarantee as the value of a European Put Option. A surrender guarantee would have some similarities to an American Put Option. If the guarantee is payable on death then this isn't an investment guarantee and we wouldn't use the approaches described in Chapter 23 (instead the insurer is likely to deduct a mortality charge related to the sum at risk each month). Or we could use method 2 to calculate the expected present value of the cost of the maturity guarantee using simulation as you suggest. To be market-consistent we would need to calibrate the model to market prices (a risk-neutral calibration) and use the risk-free rate to project the assets and discount the costs. Alternatively we could use method 2 with a real world calibration and set the charges so that there was a high probability that charges exceeded costs. Although the choice of probability here is subjective. If there is a guaranteed surrender value then the stochastic model can be adjusted to allow for the probability of surrender each year. The probability of surrender will be related to the investment performance as policyholders are more likely to surrender when investment returns are low. But the overall principle is the same - we perform lots of simulations and calculate the cost (if any) in each simulation. Best wishes Mark
Thank you for the reply. With simple maturity guarantees, we simply need to discount the cost of the option indicated by the simulations (there is only one value to discount). My main confusion was if we have a guarantee that is investment linked that can effectively be paid on death (and death can occur at any time). In this case, there is just not a single value to discount. So should we discount the resulting cost at the end of every year? (I see the example I provided was not exactly the best thought out example - my apologies )
Hi Chapter 23 introduces the two methods (option pricing and simulation) for costing investment guarantees such as a guaranteed minimum maturity value or a guaranteed minimum surrender value. For example, a unit-linked policy may pay the greater of the unit value or the sum assured at maturity. Guaranteed amounts payable on death are not investment guarantees, so we wouldn't use the approaches described in Chapter 23. A common unit-linked death benefit may be the greater of the unit fund or the sum assured. The insurer could charge for this annually using the formula q_x * Max(sum assured - unit value, 0). You say above that the guarantee is investment linked. If the death benefit is equal to the unit fund then there is no sum at risk and no need to have any charge. Let me know if you were thinking of something else. Best wishes Mark
I see the confusion. I think this will better suit the situation. Say we have a unitised accumulating with profits policy. Regular bonuses are declared monthly and may be zero but never negative. In this case, the death benefit is payable at anytime and forms an investment guarantee since we may experience a decline in assets but cannot reduce the benefits. Effectively at the end of each year there is a cost of the guarantee since the assets may fall but we declare a 0% increase. (There is no single maturity value like we dealt with earlier). How should we then price the investment guarantee into the premiums using stochastic simulation? As a start, we would start to project the assets and the fund/benefit value using the company's bonus distribution philosophy. We cannot possibly use options as we would require numerous put options - each corresponding to the end of each year with differing strike prices based on the accumulated fund value.
Hi Thanks for the more detailed example. As this policy is with-profits, then the most likely way of dealing with this is through the asset share. Any overpayment of the death benefit compared to the per policy asset share would then be spread over the asset shares of other policies. There could be other ways of structuring this policy and a lot depends on who carries the mortality risk (the policyholders, the insurer, or a combination), but that feels beyond the SP2 course. However, we could model the policy stochastically. Each simulation would simulate the investment return each year and would simulate the time of death too. Best wishes Mark
Hi A final thought on this. What you are describing isn't an investment guarantee as covered by the SP2 Core Reading. SP2 mentions maturity guarantees, surrender guarantees and guaranteed annuity options. So the death benefits you are mentioning fall outside the scope of Chapter 23. Best wishes Mark
