Understanding the behavior and hedging of segregated funds offering the reset feature

North American Actuarial Journal, Apr 2002 by Windcliff, Heath, Roux, Martin Le, Forsyth, Peter, Vetzal, Kenneth

As shown in Figure 6, the degree of optimality displayed by investors has a large impact on the required hedging costs of these contracts. Why is it so expensive to hedge a contract that is reset optimally? Investors who reset optimally are more likely to catch the peaks in the market and, thus, end up with higher guarantee levels. Alternatively, they are likely to (antiselectively) lapse much sooner, depriving the insurer of fee income.

5.2.1 Optimal Exercise Boundary

Collecting data to determine quantitatively the level of optimality is difficult and requires knowledge of the optimal exercise boundary. In other words, we could compare data on investors' use of their reset options with the optimal exercise boundary to assess whether the appropriate optimality level should be 25% (as assumed in our base scenario) or some other number. At this stage, we do not have sufficient data on the use of the reset provision by investors to do this. However, we are able to compute the optimal exercise boundary.

Figure 7 illustrates this for a contract that allows the investor one reset per annum. Note that this boundary applies only to the initial contract sold to the investor, that is, for the first use of a reset. Once the investor resets, the exercise boundary changes. A rough heuristic for the contract specifications and market parameters used suggests that these contracts should be reset when the value of the fund is approximately 10%% above the current guarantee level.'

The location of the exercise boundary depends on the current maturity date of the contract. We can see that there is a trade-off between getting a higher guarantee level by resetting and deferring the maturity date of the contract by another 10 years. The jumps in the location of the optimal exercise boundary occur because the investor receives a new reset opportunity each year.

5.2.2 Effect of Deterministic Lapsing

As mentioned earlier, for a variety of reasons investors may withdraw from these contracts independently of the value of the underlying fund. Figure 8 compares the net value of these contracts for different levels of investor deterministic lapsing. As expected, an increase in the deterministic lapse rate reduces the net cost of hedging these contracts because fewer people remain in the fund to collect any payoffs made by the guarantee. However, as seen in the accompanying table, the required proportional fee does not decrease as rapidly as perhaps anticipated. This is because, as the rate of deterministic lapsing is increased, the number of investors remaining in the fund (and, consequently, the value of the future incoming fees) decreases.

Note that the lapsation model used is very simple; some given fraction of the investors lapse out of the contract every year. This approach probably undervalues these contracts when the guarantee is deep-in-the-money. In this situation, investors would be better off remaining in the segregated fund and receiving their minimum locked-in value rather than lapsing and throwing away their guarantee.