Economic scenario generator (NAIC-calibrated)
Generate thousands of interest-rate, equity and inflation scenarios with the Academy stochastic-log-volatility equity model, test them against the NAIC calibration criteria, set the VM-20 mean reversion parameter, pick a representative subset, and compute CTE70/CTE90 stochastic reserves.
τ = 0.12515, φ = 0.35229, σv = 0.32645, ρ = -0.2488, A = 0.055, B = 0.56, C = -0.9; σ ∈ [0.0305, 0.7988]. Annual-step vol scale 1.08 keeps every official NAIC calibration point satisfied.
NAIC equity calibration criteria (AG 43 / VM-20 Appendix 1)
The official 22-point table: generated gross wealth ratios must be no richer than the left-tail points and no thinner than the right-tail points. Run 5,000+ scenarios for a stable test; a single miss by a few thousandths is sampling noise. Source: Academy VAREQ, Equity Return Calibration Criteria (June 2013), p.3 — the AG 43 / VM-20 Appendix 1 table
| Horizon | 2.5% | 5.0% | 10.0% | 90.0% | 95.0% | 97.5% |
|---|---|---|---|---|---|---|
| 1y | 0.753 / 0.78 | 0.811 / 0.84 | 0.875 / 0.90 | 1.311 / 1.28 | 1.373 / 1.35 | 1.435 / 1.42 |
| 5y | 0.659 / 0.72 | 0.752 / 0.81 | 0.868 / 0.94 | 2.189 / 2.17 | 2.538 / 2.45 | 2.801 / 2.72 |
| 10y | 0.715 / 0.79 | 0.819 / 0.94 | 0.981 / 1.16 | 3.707 / 3.63 | 4.439 / 4.36 | 5.056 / 5.12 |
| 20y | — no criterion | 1.123 / 1.51 | 1.470 / 2.10 | 9.939 / 9.02 | 12.510 / 11.70 | — no criterion |
Generated / criterion. Green = criterion met.
Seed from the real Treasury curve (GOES-style)
The NAIC generator is anchored to the current constant-maturity Treasury curve. One click pulls today's H.15 curve (3-month to 30-year), sets the 1-year CMT as the starting short rate, the 20-year CMT as the starting long rate, the VM-20 MRP as the long-run mean, and calibrates the inflation intercept to trailing CPI-U.
VM-20 mean reversion parameter — real Treasury data
20% × 600-month median 20-yr Treasury CMT + 30% × 36-month average + 50% × 3.75%, rounded to 0.25% (VM-20 §7.F). Data: Federal Reserve H.15 via FRED series GS20, monthly since 1953.
Representative scenario subset
Significance-ranked picking (Academy scenario picker approach). VM-20 allows a subset when the reserve is shown not to be materially understated.
Short-rate fan (5th–95th percentile) and median long rate / inflation
Equity total-return index (5th / 50th / 95th)
Stochastic reserve for the default term-life cohort
Gross liability outflows (benefits + expenses + commission, before premium) from the life projection discounted along every scenario's short-rate path. CTE70 is the VM-20 stochastic reserve statistic; CTE90 approximates a capital level.
Percentile table
| Year | Short 5% | Short 50% | Short 95% | Long 50% | Equity 5% | Equity 50% | Equity 95% | Inflation 50% |
|---|---|---|---|---|---|---|---|---|
| 0 | 4.30% | 4.30% | 4.30% | 4.20% | 1.00 | 1.00 | 1.00 | 2.50% |
| 5 | 0.55% | 3.38% | 7.23% | 3.95% | 0.75 | 1.38 | 2.54 | 2.18% |
| 10 | 0.15% | 3.07% | 7.46% | 3.85% | 0.82 | 1.95 | 4.44 | 2.03% |
| 15 | 0.11% | 2.84% | 7.53% | 3.79% | 0.93 | 2.71 | 7.78 | 2.04% |
| 20 | 0.10% | 2.83% | 7.89% | 3.78% | 1.12 | 3.75 | 12.51 | 1.99% |
| 25 | 0.10% | 2.74% | 7.76% | 3.73% | 1.28 | 5.40 | 21.10 | 2.11% |
| 30 | 0.10% | 2.79% | 7.89% | 3.79% | 1.62 | 7.23 | 32.43 | 1.98% |
Live endpoint — deploy this generator
The same generator is hosted at POST /api/public/v1/esg: send years, scenarios, seed and (optionally) anchors or liability cash flows; get rate/equity/inflation percentiles, the NAIC calibration check, CTE70/CTE90 and sample paths back. Omit the anchors and the endpoint seeds itself from the live FRED curve. Seeded runs are reproducible, so a scenario set can be cited by (seed, version).
curl
curl -X POST /api/public/v1/esg \
-H "Authorization: Bearer $ACTUARIUM_KEY" -H "Content-Type: application/json" \
-d '{"years":30,"scenarios":1000,"seed":2026,"equityModel":"airg-slv","useTreasury":true,"samplePaths":2}'- Equity: the Academy Interest Rate Generator (AIRG) stochastic-log-volatility model with its published US-diversified-equity parameters, stepped monthly and aggregated to years, tested against every NAIC/VM-20 calibration point on this page. Rates: a two-factor mean-reverting model reverting to the VM-20 MRP with a floor. The NAIC GOES (Conning) generator itself is a licensed download whose parameter files are not redistributed here; this generator satisfies the same acceptance criteria and exposes the same statistics (percentile fans, calibration table, CTE70/CTE90, scenario subset).
- Rate/equity correlation −0.25 and short/long shock correlation 0.6 are fixed; change the code constants to stress them.
- Stochastic reserve ignores dynamic policyholder behaviour and reinvestment strategy; it is the discounted-liability CTE, not a full asset–liability projection.
- Results are seeded and reproducible; increase scenarios to 5,000 for stable CTE90 estimates.