Industry: Insurance and Reinsurance Product: ModelRisk Application: Modeling Policyholder Behavior
A 240,000-policy universal-life block with $11.5B of account value and a 3.0% guaranteed crediting rate is the kind of asset that looks placid right up until the moment market rates spike past the credited rate by 300 basis points. Then dynamic surrender behaviour — policyholders cashing out the AV to chase higher yields elsewhere — turns a stable block into a billion-dollar liquidity event over the following two years. The deterministic actuarial model, with a flat assumed lapse rate of 6.6% per year, says nothing useful about that scenario, because the answer is not a number, it is a behavioural response function whose elasticity is itself uncertain.
A life carrier with a major in-force UL portfolio rebuilt its lapse and surrender model in ModelRisk. The driving need was to put dynamic behaviour at the centre of reserve-adequacy and product-design decisions instead of carrying it as a static appendix to the asset-liability projection — and to express both the expected behaviour and the uncertainty about that behaviour explicitly. Run the same behavioural engine across four interest-rate paths and the spread between them is the whole story: the 10-year present value of surrender outflow shifts from a mean of roughly $5.1B in the baseline to $7.0B once a rate shock hits at year 3, with the upper tail pushing toward the size of the block itself.
The model decomposes the realised surrender rate per year into a base component plus a dynamic excess driven by the gap between market rates and the credited rate net of surrender charge:
\[ L_t = L_0 \cdot D + \delta \cdot \max(r^{\text{mkt}}_t - r^{\text{credited}} - \text{spread},\ 0) \]
with three uncertain inputs:
Base lapse rate \(L_0\) is modelled as Beta(2.5, 35) ≈ mean 6.6% with substantial dispersion. Beta is the right family because lapse rates are bounded on [0, 1]; modelling lapse as a Normal — which several in-house ALM models still do — lets the simulator draw negative or above-100% lapse rates, which is meaningless on the face of it and corrupts every downstream cash-flow projection.
Dynamic-surrender elasticity \(\delta\) is LogNormal with median 2.5 and σ on the log scale of 0.35 — right-skewed because behavioural responses to large rate excesses are themselves heavy-tailed (a small minority of policyholders are highly rate-sensitive). The mean of 2.5 means that a 100bp rate excess above the credited-plus-spread floor adds about 2.5 percentage points to the annual surrender rate at the central estimate, but the tail of \(\delta\) carries that adder past 5pp in stressed scenarios.
Demographic factor \(D\) is Triangular(0.85, 1.00, 1.30), capturing the cohort effect (younger, less financially established policyholders surrender more readily than older policyholders with mature policies).
These three distributions are coupled across trials by a Gaussian copula — economic stress that drives up \(\delta\) is correlated with the demographic factor through unemployment, so treating them as independent (the previous spreadsheet model's assumption) systematically understates joint stress.
The 10-year present value of surrender outflow was simulated under four macroeconomic scenarios: a baseline at ~3.5% (mean $5.1B, P95 $8.2B), a low-for-long path averaging 2.2% (mean $4.6B, P95 $8.0B), a gradual rise from 4% to 6% (mean $6.6B, P95 $8.9B), and a sudden spike at year 3 from 3% to 7.5% (mean $7.0B, P95 $9.1B). The same behavioural engine produced four distributions, overlaid in the opening chart.
The baseline and low-for-long curves sit close together, because the behavioural response is bounded by the base lapse rate when market rates are below the credited-plus-spread floor. The rising path moves the distribution out by roughly $1.5B in mean PV terms. The shock spike at year 3 pushes it furthest — its mean runs about 1.4× the baseline and its upper tail climbs toward the full account value, because the trial-by-trial \(\delta\) draw amplifies the spike for the rate-sensitive subset of trials. Note that both distributions are already wide before any shock, because the base lapse rate itself is uncertain trial-to-trial — which is why the shock shifts the mean more than the P95.
The carrier's prior deterministic asset-liability model, run on the same scenario with a flat 6.6% lapse assumption, produced a "shock-scenario surrender outflow" of about $5.0B PV. The Monte Carlo run on the same scenario says:
Mean shock-scenario outflow is $7.0B — about 1.4× the deterministic figure; the VaR 95% sits at $9.1B, roughly 1.8× the static point estimate; and the right tail runs past $10B, approaching the entire account value of the block — a near-total-surrender stress the flat-rate model treated as impossible. The static model was wrong by exactly the dynamic component it could not represent — which is to say, by the part of policyholder behaviour that actually matters in a stress.
Dynamic-surrender elasticity \(\delta\) dominates — its uncertainty alone is responsible for the majority of the P95 spread. That tells the product and ALM teams the highest-value analytical project is direct behavioural research: policyholder surveys, A/B-tested retention campaigns, and matched-cohort analysis of the carrier's own historical surrender response to past rate moves. Rate-path magnitude ranks second, which is partly outside the carrier's control but is the input to which the hedging programme is being sized. Base lapse \(L_0\) ranks third — meaningful, but markedly less leverage than the dynamic term, which contradicts the long-standing internal assumption that "lapse risk = uncertainty in \(L_0\)."
The point the actuarial team kept making after the deployment: lapse risk is not the uncertainty around the base rate — it is the joint distribution of base rate, elasticity, and rate path, and Monte Carlo is what binds those three into a single number the CFO can read off the page when the regulator asks how much capital the surrender tail consumes.