Valuation of segregated funds: shout options with maturity extensions

One of the most popular investments available in the Canadian market today is a mutual fund with the added feature of a long term maturity guarantee. These types of investments are known as segregated funds. They often have very complex option features. For example, these contracts typically contain multiple embedded shout options which permit the holder to reset the guarantee level and the maturity date for which it applies many times during the life of the contract. These funds also provide mortality benefits if the investor dies prior to the maturity date. This paper explores the valuation of segregated funds using an approach based on the numerical solution of a set of linear complementarity problems. Our results indicate that the option components of some of these contracts seem to be underpriced, especially for riskier funds with relatively high volatilities. This assumes that investors exercise their options optimally. Non-optimal behaviour by investors of course reduces the values of the embedded options, and we provide some illustrative results along these lines. We also show that alternative contract specifications which generate similar present values may require substantially different proportionate fees, since the expected durations of the contracts can be quite different.