Duration Gap and a 250bp Tightening Cycle
EuroLife, a UK life insurer, holds £5.0bn of fixed-interest assets with a modified duration of 9.2 years and £4.8bn of annuity liabilities with a modified duration of 13.5 years. It holds no interest rate derivatives. Over twelve months the central bank raises its policy rate by 250 basis points in response to inflation of 6.4%. The 10-year government yield rises from 3.1% to 5.0% while the 2-year rises from 3.4% to 5.6%, inverting the curve. EuroLife's internal model uses a single parallel 100bp shock calibrated to a 1-in-200-year event. During the same period, lapse rates on its unit-linked bond book rise from 6% to 11% a year, and annuity new business volumes rise 40% as customers seek guaranteed income. The chief risk officer asks whether the internal model is still adequate and how the rate rise should flow through to liability cash flows.
1. Assess the adequacy of the 100bp parallel shock given the duration gap, and propose a more appropriate interest rate risk model.
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Using modified duration:
- Assets: change in value ≈ −9.2 × £5.0bn × 1.9% ≈ −£874m.
- Liabilities: change in value ≈ −13.5 × £4.8bn × 1.9% ≈ −£1,231m.
The surplus improves by roughly £357m when yields rise: EuroLife is net short liabilities. The 100bp shock understates the 190bp ten-year move, and more importantly assumes a parallel shift while the curve inverted (2-year +220bp, 10-year +190bp). Key-rate exposures differ: liabilities are long-dated while asset duration is 9.2, so 20- and 30-year rates matter most. Convexity also matters for a move of this size.
A better model uses key-rate durations or a full curve model (for example Hull–White, or a Nelson–Siegel factor model) calibrated to swaptions, with stochastic scenarios rather than a single deterministic shock. The 1-in-200 calibration should be re-estimated from current volatility. Include the gilt–swap basis, the liability discount basis (+0.3%), and management actions. Report non-parallel stresses - steepener, flattener and inversion - separately.
2. Explain how the rate rise could affect policyholder behaviour and how this should be reflected in the liability model.
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Higher rates change behaviour in at least three ways:
- Unit-linked bond lapses rose from 6% to 11% because policyholders can get better returns elsewhere. Each lapse removes future charges, so the insurer loses future profits even though the liability falls. This is a dynamic lapse effect: lapses depend on the gap between the policy's credited rate and competitor rates, not on a fixed assumption.
- Annuity new business rose 40% as customers locked in higher guaranteed income. This lengthens new liability duration and reinforces the asset-liability mismatch.
- Persistency of in-force annuity business may improve, but mortality and longevity risk remain separate.
The liability model should replace static lapse assumptions with a dynamic lapse function estimated from experience, with thresholds and asymmetry (lapses rise when rates rise but do not fall symmetrically when rates fall). The function must be driven by the same economic scenarios as the asset model - an economic scenario generator linking interest rates, inflation, equity returns and lapse behaviour - so that asset and liability results are consistent. Otherwise the model will understate the loss of future profits in rising-rate scenarios.
3. Recommend how EuroLife should manage the asset-liability position, considering cost and capital.
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The duration gap is the central issue: liabilities 13.5 years against assets 9.2 years. Options:
- Buy long-dated fixed-interest gilts or receive-fixed interest rate swaps to extend asset duration. Receiving fixed increases duration and gains if rates fall, offsetting liability increases.
- Use a partial hedge rather than full matching: full matching is costly and removes upside. The board should set a target duration gap consistent with risk appetite.
- Plan for collateral: receive-fixed swaps lose value when rates rise and require margin. The insurer must hold liquid collateral; a rise of the size seen would have produced collateral calls.
- Review the liability discount basis and any matching adjustment eligibility before changing the portfolio, so that assets and liabilities are valued consistently.
- Stress a 200bp fall as well as a rise: the same duration gap that helped here would hurt badly in a rally.
Recommendation: extend duration materially using a liquid, collateral-efficient structure, document the target gap, and recalibrate the internal model to key-rate and stochastic shocks.