Comonotonic approximations to quantiles of life annuity conditional expected present value

In large portfolios, the risk borne by annuity providers (insurance companies or pension funds) is basically driven by the randomness in the future mortality rates. To fix the ideas, we adopt here the standard Lee-Carter framework, where the future forces of mortality are decomposed in a log-bilinear way. This paper aims to provide accurate approximations for the quantiles of the conditional expected present value of the payments to the annuity provider, given the future path of the Lee-Carter time index. Mortality is stochastic while the discount factors are derived from a zero-coupon yield curve and are assumed to be deterministic. Numerical illustrations based on Belgian mortality (general population and insurance market statistics) show that the accuracy of the approximations proposed in this paper is remarkable, with relative difference less than 1% for most probability levels.