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# On-Risk and Off-Risk Age

In many of the GMDB products offered, insurance companies typically have age restrictions associated with them. On the deposit side, the insurance companies typically require that the annuitant cannot exceed a certain age before the basic product (and its rider) can be issued. Furthermore, even after issuance, an insurance company may have restrictions on cutoff age after which no additional deposits can be made into the policy. These are sometimes called on-risk age. In addition, riders quite often come equipped with the notion of off-risk age. As described by the name, off-risk age refers to the age beyond which the rider no longer rolls up or ratchets.

From a pricing standpoint, it is important to be able to embed these features into calculations so that the frequency and cut-off time associated with the roll-ups and ratchets are more accurately captured.

# Investment Allocation

In my discussion thus far, I have conveniently assumed that the policyholder makes an investment in one fund. In practice, insurance companies offer a multitude of funds (sometimes hundreds of them) in which the policyholder can allocate investments. The inputs required to value the optionality embedded in the basic product and its riders when there is only one fund are the fund fee, fund growth rate, and fund volatility rate. In the event the policyholder invests in a multitude of funds, the fund values, growth rates, and volatilities associated with each of these funds (in addition to the correlation between the fund returns) become instrumental in helping to determine the value of the optionalities.

Since how well the total investment in a GMDB product performs is really a function of how the investment is distributed among all the available funds, the insurance company is left with the task of guessing at this distribution. Clearly, the more accurate the predicted breakdown of investments among the policyholders, the lesser the risks exposed to when making these assumptions. The biggest risk the insurance company is exposed to when doing this is to assume that all the investments are deposited into a money market fund, only to experience that all policyholders have actually made their investments into a fund that has the highest volatility. Over the last decade, in order to reduce the risks embedded in these products, insurance companies have introduced restrictions into the types of funds a policyholder can allocate the investments into if certain types of riders (including living benefits) are chosen.

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