Survivor Swaps

Abstract

A survivor swap (SS) is an agreement to exchange cash flows in the future based on the outcome of at least one survivor index. This article discusses the possible uses of SSs as instruments for managing, hedging, and trading mortality-dependent risks. SSs are especially useful for insurance companies, but also offer other interested parties low beta avenues into the acquisition of mortality risk exposure. The article also investigates vanilla SSs in some detail, and suggests how their premiums and values might be determined in an incomplete market setting. Copyright The Journal of Risk and Insurance, 2006.

Options on normal underlyings with an application to the pricing of survivor swaptions

“…If we accept this line of reasoning, then the sets of b distribution parameters presented in Table 1 of Dowd et al (2006) lead us to believe that the most plausible representation of mortality given in that Table is their case 1: this is where (i) has a zero mean and a standard deviation of around 2.2%, and this occurs where the b distribution has parameters a ϭ b Ϸ 1,000. Thus, if we accept this example as plausible, 3 we might expect the parameters of the b distribution to be both high and approximately equal to each other.…”

“…, (t). Dowd (2005, p. 5) then suggests that the longevity shocks (1), (2) The premium p is set so that the initial value of the swap is zero, and, in the case of a the simple vanilla swaps considered in Dowd et al (2006), this implies that (22) where is the value of the fixed leg and is the value of the floating leg, and l i is the probability of survival to i. Equation (22) tells us that, in general, the swap premium is related to a weighted average of the expectation of n Ϫ 1 independent (i) shocks, each of which follows a transformed b distribution.…”

“…This takes us to the distribution of (i) itself. In their original study, Dowd et al (2006) suggested that the size of p reflected projected longevity improvements since the time that the pre-set leg of the swap was initially set. In the past, the pre-set leg would typically have been based on projections from a mortality table that was prepared years before and projected fairly small mortality improvements.…”

“…History suggests that when linear payoff derivatives succeed, there is generally a requirement for option-based products to develop as well. This study derives a risk-neutral approach to pricing and hedging options on survivor swaps, building on the survivor swap pricing model published in Dowd, Cairns, Blake, and Dawson (2006) (henceforth, Dowd et al, 2006).…”

“…Central to the option model is the observation that the random survivor premium, p, in Dowd et al (2006) is (at least approximately) normally distributed. Normal distributions have generally been shunned in asset pricing, as they permit negative prices.…”