Why is the lower band of std. deviation of the expected payout so low for 105 years old? (page 7, chart) Why does it go down at all starting from 98 years old?
As for the widening deviation in the payout charts in very advanced ages, the answer lies in the degree of longevity risk pooling provided at various stages of a tontine’s life. In the early years of the tontine, the member of members is quite large and therefore actual mortality experience will tend to be close to that which is expected (central limit theorem). Over time, members pass away and the pool becomes smaller… gradually at first and then more quickly in very advanced ages as the “force of mortality” becomes more substantial. With a smaller pool, the potential for actual mortality to deviate from that which is expected grows as well, meaning that the benefit of risk pooling diminishes. In the case of the lower standard deviation line, then, this would represent scenarios in which a significant portion of the pool of tontine members stubbornly fail to die at the rate expected per the mortality tables (perhaps also accompanied by a simulated period of low investment returns). In such an scenario, the tontine must govern its payout to reflect the actual experience of both the portfolio and the actual number of members still alive.
Note that we modeled the tontine as a closed structure (initially open to members aged 65-70, but then closed to new members after that). It is certainly possible to design fair tontines that are instead perpetually open-ended. Open-ended tontines would alleviate the issue of a gradually declining number of members and the corresponding reduction in the mortality pooling effect. So, one would expect the range of outcomes to be narrower in an open-end structure. The question then is whether people would feel comfortable investing in a tontine that includes members with a very wide range of ages (e.g., 65-110+). And since tontines are going to be a new concept to most people, the closed-end route may represent the best entry point for introducing these products back into the market.
The above also helps explain why guarantees are so expensive. The guarantor must take into account every possibility. That pushes down the amount of income the guarantor can offer. You really have to value the "fixed no matter what" guarantee in order to prefer it to collectively self-pooling the risk in a tontine.
We are conducting a large number of simulations that include investment volatility as well as random mortality (according to mortality tables), so that each member will expire at a certain unpredictable time in each simulation.
What results is a range of possible payout streams, and you saw the distributions on the chart. The system is monitoring the situation constantly, and will be making tiny, hardly perceptible adjustments in real time always with an eye to the end of the tontine.
We will continue to conduct simulations with a variety of input variables to make sure that the system can handle whatever is thrown at it.