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Wildfire Insurance → Investigation 03

What’s the Correlated Tail Risk?

Fire occurrence and fire severity share weather regimes. In a bad year, fires are more likely AND more aggressive. We simulated 200 fire seasons under correlated and independent assumptions.

200 Seasons Simulated
30 Neighborhoods
1.43x P99 Amplification

Q2 showed that a single WUI neighborhood has a PML99 of $2.3B — exceeding its total insured value. But insurers don’t hold one neighborhood. They hold portfolios. The question becomes: when multiple neighborhoods face fire simultaneously, does the portfolio diversify the risk — or concentrate it?

The Problem

Why Independence Understates the Tail

Single-fire models capture individual fire risk. But insurers hold portfolios. In reality, drought and wind events that make one fire likely make all fires in the region more severe. Treating fires as independent understates the tail.

A Diablo Wind event doesn’t affect one canyon — it affects every canyon in the fire weather zone simultaneously. The same Santa Ana condition that drove the Camp Fire also elevated risk across the entire Northern California WUI. When you model each neighborhood independently, you miss the scenario where everything burns at once.

Monte Carlo — 200 Seasons

Portfolio Loss Exceedance Curve

Portfolio Loss ($M) vs. Exceedance Probability
Finding
The correlated and independent models produce similar average losses ($5.2B vs $5.1B). But correlation concentrates risk: in a bad year, everything burns at once. The 1-in-100-year loss is 43% worse under correlated weather ($20.6B vs $14.4B).

Both curves use identical property data, identical fire behavior models, and identical loss functions. The only difference is whether each neighborhood draws its weather independently or shares a common weather regime. The means are nearly identical ($5.2B correlated vs $5.1B independent). But at the 1-in-100-year level, the correlated model diverges: $20.6B vs $14.4B, a divergence of $6.2 billion.

Model: 200 simulated fire seasons, 30 neighborhoods, L3 Rothermel fire spread. Correlated model uses shared weather regime with 15% “bad year” probability.

Tail Risk

1-in-100 Year Season Loss

P99 Season Loss ($M) — Correlated vs. Independent

The bar chart isolates the tail. In the independent model, the 1-in-100-year season produces $14.4 billion in losses. In the correlated model, the same probability threshold produces $20.6 billion — an additional $6.2 billion that doesn’t appear in any average-year analysis.

Finding 3
At the portfolio level, the correlated model produces a P95 of $14.2B vs. the independent model’s $10.7B — a 32% amplification. The divergence grows with return period: 2% at the mean, 16% at P90, 32% at P95, 43% at P99. Reinsurers who price at P90 would underestimate by 16%. Those who price at P99 would underestimate by 43%.
The Mechanism

How Correlation Amplifies the Tail

Bad year (15% probability): fires are 3x more likely AND 50% windier/drier. In the correlated model, all 30 neighborhoods face elevated risk simultaneously. In the independent model, each neighborhood draws its own weather — averaging out the extremes.

The correlated model works in two stages. First, it draws a season type: 85% of years are “normal,” 15% are “bad.” In a bad year, every neighborhood in the portfolio faces the same elevated fire weather — higher wind speeds, lower fuel moisture, more ignition sources.

This matches reality. The 2017 fire season (Tubbs, Thomas, Nuns) and the 2018 season (Camp, Woolsey) were not collections of independent events. They were driven by persistent atmospheric patterns that elevated risk across the entire state for weeks.

The independent model smooths out catastrophe. When each neighborhood draws its own weather, the probability that all 30 see bad conditions simultaneously is 0.1530 ≈ 0. In reality, that probability is 15% — because they share the same atmosphere. The independent model doesn’t understate average risk. It understates the risk that matters for solvency.

Finding
Correlation modeling barely changes the expected loss — but it changes the capital requirement. An insurer using independent fire models will hold 30% less capital than the correlated model demands — and will be insolvent in exactly the year that matters.
Amplification

Correlation Amplification by Return Period

Amplification Ratio (Correlated / Independent) by Return Period
Finding
Correlation amplification grows with return period — invisible at the mean (1.02x), modest at P90 (1.16x), and significant at P99 (1.43x). This is why single-fire models produce adequate pricing but underestimate capital requirements. The capital requirement is set by the tail, and the tail is where correlation lives.
Sensitivity

Correlation Strength vs. Capital Impact

If Correlation Is... Portfolio P99 P99 Ratio vs Independent Capital Impact
Zero (independent) $14.4B 1.00x Baseline
Moderate (0.5) ~$17.5B ~1.21x +21% capital
Full (1.0, our model) $20.6B 1.43x +43% capital

Our model uses full correlation within a season regime (all neighborhoods share the same weather). Reality is between moderate and full — weather regimes are regional, not statewide. The 1.43x ratio is an upper bound; real-world amplification is likely 1.2–1.4x.