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

5. VARIATIONS

Our model takes several important input parameters from the market. For example, the cost of providing the guarantee will depend on the volatility of the fund for which the guarantee is being provided. Other important factors include the risk-free rate and the level of optimality displayed by investors.

5.1 Effect of Volatility and Risk-Free Interest Rate

One very important parameter we must estimate from the market when valuing these guarantees is the volatility of the underlying fund. In this paper, we give results for simple constant volatility models. The base scenario uses a volatility of a = 17.55%. Guarantees offered on more volatile funds can be dramatically underpriced. Figure 4 plots the residual cost, net of future incoming fees, of providing a segregated fund guarantee given the fixed fee, re = 50 bp for various levels of volatility. For guarantees written on higher volatility funds, the residual cost, net of incoming fees, is positive. This indicates that the insurer will not be able to cover the costs of dynamic hedging with this choice of re. Figure 4 also contains a table showing the proportional fee that should be charged in order to cover the hedging costs for the given volatilities.

Another important parameter in the model is the risk-free interest rate. Figure 5 demonstrates that small changes in our assumptions about the risk-free rate can have dramatic impacts on the cost of providing these guarantees. Our assumptions that the interest rate and volatility are constant are clearly unrealistic, especially given the long-term nature of these contracts. In practice, we would have to consider carefully how to estimate these parameters in order to minimize the effects of these simplifying assumptions. For example, we would probably want to use a volatility parameter that is consistent with prevailing implied volatilities from options markets, rather than the historical volatility of the underlying funds in question.

These results might be viewed as conservative in that we are assuming a degree of investor optimality of 25%. The effect of investor behavior is discussed in the next section. Typically, segregated funds are sold with a value of re in the range of 40-80 bp. In view of the results in Figures 4 and 5, we can see that these fees are appropriate for low-to-moderate volatility funds and interest rates that are not very low, even assuming that investors do not use their reset options with a high level of efficiency.

5.2 Effect of Investors' Behavior

Another very important parameter our model uses is the level of optimality displayed by investors when using the reset feature. Strictly speaking, from a no-arbitrage viewpoint, one should assume that investors act optimally. In practice, most investors do not act in this way, and we would like to incorporate this into our model.

Note that, by assuming that investors act nonoptimally and charging fees based on this, insurers expose themselves to three additional sources of risk. First, these contracts are extremely long term and it is possible that there may be secular changes in investors' behavior over the life of the contract. Similar changes are known to have occurred in other contexts, for example, prepayment rates on mortgages in the United States. Second, there may be considerable uncertainty about the current level of investor optimality, since few insurers appear to be in a position to measure this with any degree of rigor. Third, it may be possible for a single knowledgeable investor to take a relatively large position, affecting our assumption about the level of optimality displayed by investors.