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

Limiting the value of the guarantee to 75% of the current level of the asset does reduce the hedging cost substantially. The value of the resulting contract is relatively less sensitive to optimal investor behavior, but more sensitive to high volatility.

If the correct proportional fee, re, is being charged, handling resets by imposing a minimum value constraint at zero can be an accurate approximation. This approximation allows these contracts to be valued in the time required to value a standard American put option. However, care must be taken if the proportional fee being charged is too small.

The results given in this paper can be viewed as the minimum cost of providing these guarantees since we are modeling a contract that has much less optionality than many existing marketed contracts, and we have assumed a low degree of investor optimality. Also, additional reserves may be required to handle unhedged risks such as basis risk, volatility risk, and interest rate risk as well as transactions costs.

ACKNOWLEDGMENT

This work was supported by the Natural Sciences and Engineering Research Council of Canada, the Social Sciences and Humanities Research Council of Canada, RBC Financial Group, and Sun Life Financial.

1 According to the consulting firm Investor Economics (2000), the total amount of individual segregated fund contracts issued by Canadian insurers was $45 billion (CDN) as of August 2000, up from $9 billion at the end of 1995. Forty-seven percent of these assets had a maturity guarantee of 100%. Note that, although not every insurer provides optionality such as reset provisions, many of them either do or did at one time.

2 Extensive treatments of financial option valuation can be found in texts such as Hull (2000) or Wilmott (1998).

3 See Boyle and Hardy (1997) for a discussion of these issues in the case of simple maturity guarantees, without reset provisions.

4 This interpretation assumes that the sizes of investor accounts are approximately equal. More accurately, we assume that, of the total units of fund we are guaranteeing, over a year, 25% of the guarantees are reset when it is optimal to do so.

5 As mentioned above, a DSC is applied to investors' accounts during the first five years of the contract. This effectively provides a penalty for lapsing during this time, as investors lose a percentage of the value of their accounts if they close them. This obviously reduces the chances of antiselective lapsation.

6 This ignores the mortality aspect of the contract. As noted earlier, for the investor demographic type we are considering, this feature does not have significant value.

7 This assumes a "delta-neutral" hedging strategy. In theory, this is all that is needed, but it does assume continuous adjustment of the hedging position. In practice, positions can only be adjusted discretely. A more sophisticated approach that attempts to account for this is a "gamma-neutral" strategy. This would require holding a position in other options, even if the position has A - 0. Readers interested in further details about this type of hedging should consult texts such as Hull (2000).