Longevity swaps

A pension cohort's realised survival against the best estimate plus a risk premium, with Lee-Carter mortality improvement paths on a Gompertz-Makeham base table; value, the 99.5% worst case, the longevity stress, fair premium and survival percentiles by year.

Inputs

Position

Pensioners

Pension a year

Age

Termyears

Mortality improvement%

Improvement vol%

Age slope of b(x)

Risk premium%

Longevity stress%

Paths

CurrencyCurve

Curve: flat rate% cc

Results

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Methodology

Conventions

The floating leg pays the cohort's realised survival a year, the fixed leg the best estimate times (1 + premium)^t.
Lee-Carter: ln m(x, t) = ln m₀(x) + b_x k_t, k_t a random walk with drift, base mortality Gompertz-Makeham.
The stress lowers mortality by the shock (Solvency II longevity stress).

References

Lee and Carter (1992)
Biffis and Blake (2010)

Formulas

Lee-Carter: ln m(x,t) = a_x + b_x k_t, k_t = k_{t−1} − g + σε