FXP Stock Trading

Guaranteed Minimum Maturity Benefit

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In this section, we show how to generate the distribution of the present value of the guarantee liability for a simple GMMB policy held by a life aged x with remaining duration n years. We assume a monthly discrete time model for equity returns and management charges. Withdrawals and deaths are assumed to occur at month ends. As discussed, exits are treated deterministically, so the only random process simulated is the equity price process.

Clearly other assumptions and approaches are possible; the aim here is to demonstrate the basic principles. Since St is a stock index, we assume S0 = 1.0 so that St is the accumulation factor for the period from time 0 to time t. Recall that (G - Fn)+ = max(0, G - Fn). Then,

Then, n

So Ct and L0 can be calculated for each stock index scenario, and distributions for the cash flows in different years and for the present value random variable can all be simulated.