Longevity Model Validation and the Use Test
Helios Life Re's internal model prices and hedges longevity swaps and determines economic capital for its annuity book. The longevity module uses a two-factor CBD stochastic mortality model calibrated to 12 years of national population data, with an expert-judgement overlay for cohort effects. The latest validation found four backtesting exceptions at the 99% level over the last 12 years, where 0.12 were expected; the model owner attributes this to data scarcity and says the model remains 'directionally right'. The model output drives a $1.4bn hedging programme and a regulatory capital figure that is 22% below the standard-formula result. The regulator's model review has issued a finding that the use test is not adequately evidenced and has requested a remediation plan within 30 days. Separately, the model is being extended to price a new bulk-purchase annuity transaction worth $600m. The CRO must decide whether to recalibrate, overlay margins, restrict model use, or some combination, and how to present this to the board without triggering a loss of confidence.
1. Diagnose the likely causes of the backtesting failures and assess the materiality of the model risk, distinguishing between calibration error, model structure error and data limitations.
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Four exceptions at 99% over 12 years is far above the expected 0.12 and suggests either the tail is mis-specified or the calibration window is too benign. Possible causes: (a) structural - a two-factor CBD model may not capture cohort or volatility effects; (b) calibration - 12 years of national data may miss scheme-specific mortality improvement and may not reflect the insured population; (c) data - a small sample with no exposure to severe events; (d) the expert overlay is opaque and may be double-counting. Materiality is high: the model drives $1.4bn of hedging and a capital figure 22% below standard formula; a 10% understatement of longevity capital would be significant. The use test also fails on evidence: there is no documented challenge log. I would not accept that 'directionally right' is sufficient; a model used to price a $600m BPA must be credible at the tail. I would rate model risk high, commission independent validation, and apply an interim capital add-on until remediation is complete.
2. Recommend a remediation plan for the 30-day regulator response, including interim controls, and explain how each action preserves or restores the use test.
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The 30-day response should: (1) acknowledge the finding and provide a dated plan; (2) impose an immediate capital add-on of, say, 10% of longevity capital until recalibration is validated; (3) suspend use of the model for pricing new BPA transactions above $100m, or apply a conservative margin; (4) commission independent recalibration using a longer window and insured-population data, and test alternative structures such as adding a cohort parameter; (5) document the use test by creating a model risk committee with challenge minutes and linking model changes to hedging decisions; (6) run sensitivity and stress tests on the hedging programme. Restoring the use test means showing that the model is used, challenged and understood, not merely that it produces a number. The add-on protects capital while the model is fixed; the pricing restriction protects against writing mispriced business. Progress should be reported monthly to the board risk committee, with the regulator kept informed of milestones.