Why Catastrophe Model Architecture Matters
A catastrophe model is not a single loss formula. It is a linked system that represents possible events, estimates the hazard those events create, translates hazard into damage to insured property, and applies financial terms to convert damage into payments. Its architecture matters in ratemaking because an error or mismatched assumption at any stage can flow through to the final loss indication.
For example, an event can be generated at the correct frequency but still produce an unsuitable price indication if the exposure values are misstated, vulnerability is inappropriate for the property, or policy terms are applied at the wrong aggregation level. A useful review therefore follows the flow of information through the model rather than treating the final expected loss as an isolated number.
The Main Modules and Their Interfaces
The modules are conceptually distinct, even when a software system combines them. Each module consumes specified inputs and produces outputs for the next stage.
- Stochastic event generation. This component represents possible events and their occurrence behavior. Its output identifies modeled events and the frequency or probability assigned to them. The purpose is to represent a range of plausible outcomes, not merely to replay the historical events in a short observation period.
- Hazard. For a modeled event, the hazard component estimates the physical intensity or effect at relevant locations. The form depends on the peril and model design; for example, the output might be an intensity measure or a spatially varying event footprint. The hazard value is not itself an insured payment.
- Exposure. Exposure information describes the insured property or assets to which the hazard applies. At a high level, it supplies the values and characteristics needed to translate hazard into potential damage. The information must correspond to the locations and coverage being modeled.
- Vulnerability. Vulnerability relates hazard and property characteristics to damage. It may represent an expected damage proportion or a distribution of possible damage outcomes. A damage estimate is not yet necessarily the insurer’s payment.
- Financial calculations. This component applies relevant insurance terms and, where modeled, reinsurance terms. It transforms damage or ground-up loss into the amounts payable by the insurer or recoverable from a reinsurer.
The model may also include data preparation, aggregation, and reporting steps. These are not substitutes for the core modules: they ensure that the inputs and outputs are consistently defined, grouped, and interpreted.
| Stage | Question it answers | Typical output passed forward |
|---|---|---|
| Event generation | What modeled events can occur, and how often? | Event identity and occurrence weight or frequency |
| Hazard | What physical effect does an event produce at a location? | Hazard intensity or event footprint |
| Exposure | What insured property and values are affected? | Values and characteristics associated with the modeled locations |
| Vulnerability | How does the hazard translate into damage? | Damage or loss before financial terms |
| Financial calculations | What amounts are paid or recovered under the contracts? | Insurer loss, insured payment, or reinsurance recovery |
From Event Frequency to Expected Annual Loss
For pricing, a model often combines event frequency with the conditional mean loss for an event. Let event type \(e\) occur according to a Poisson process with annual rate \(\lambda_e\), and let its individual event losses have mean \(\mu_e\). Let \(N_e\) be the number of events of type \(e\) in a year, and let \(Z_{e,k}\) be the loss from its \(k\)th event. The annual loss for that event type is \(S_e=\sum_{k=1}^{N_e}Z_{e,k}\).
Assume the event losses have finite mean \(\mu_e\), and that their distribution does not depend on the number of events. Conditional on \(N_e=n\), the expected total loss is \(n\mu_e\). Taking expectations over the event count gives:
Summing across event types gives the expected annual aggregate loss:
This derivation explains why event frequency and conditional severity must be interpreted together. It applies to the expected aggregate under the stated frequency and severity assumptions; it does not, by itself, describe the variability or tail of annual losses. If a model uses different occurrence assumptions, its expected-loss calculation must be consistent with those assumptions.
Worked Example: Following a Loss Through the Financial Interface
A hypothetical modeled event damages two insured locations. The ground-up damage is $90,000 at Location 1 and $40,000 at Location 2. Each location has a $10,000 deductible and a $60,000 limit on the payment for this event. The insurer’s event payment is subject to a reinsurance layer of $40,000 excess of $50,000. Calculate the policy payments, the reinsurance recovery, and the insurer’s retained event loss. State each aggregation step.
Method. First apply the policy terms separately to each location, then aggregate the resulting policy payments for the event. Apply the event-level reinsurance layer to that aggregate.
For a location with ground-up damage \(x\), the policy payment is \(\min(u,\max(0,x-d))\), where \(d\) is the deductible and \(u\) is the payment limit. At Location 1:
At Location 2:
The event payment before reinsurance is therefore \(60{,}000+30{,}000=90{,}000\). The recovery from a layer with a $50,000 attachment and $40,000 limit is:
The insurer retains \(90{,}000-40{,}000=50{,}000\). The results are $90,000 before reinsurance, a $40,000 recovery, and $50,000 retained. Common mistake avoided: applying the policy limit or the treaty to ground-up damage without respecting the stated aggregation sequence. In particular, the two policy payments total $90,000, not $100,000.
Architecture in a Stochastic Pricing Calculation
The modules can also be understood through a small hypothetical annual scenario model. In practice, modeled event sets and event losses can be much larger and more detailed. The simplified example below focuses on how occurrence probabilities, damage, policy terms, and reinsurance connect.
Worked Example: Combining Event Probabilities and Contract Terms
A hypothetical portfolio has three mutually exclusive annual outcomes: no event with probability 0.85; Event A with probability 0.10 and $200,000 of ground-up loss; or Event B with probability 0.05 and $500,000 of ground-up loss. The probabilities sum to \(0.85+0.10+0.05=1.00\). For either event, the portfolio policy has a $50,000 deductible and a $200,000 payment limit. The insurer’s payment for an event is then subject to $100,000 excess of $100,000 reinsurance. Calculate expected annual ground-up loss, expected annual policy payment before reinsurance, expected recovery, and expected retained loss.
Method. Transform each event’s ground-up loss through the policy terms, then through the reinsurance layer. Weight each result by the probability of that annual outcome.
The expected annual ground-up loss is:
For Event A, the policy payment is:
For Event B, it is:
Expected annual policy payment before reinsurance is:
The reinsurance recovery for Event A is \(\min(100{,}000,\max(0,150{,}000-100{,}000))=50{,}000\). For Event B it is \(\min(100{,}000,\max(0,200{,}000-100{,}000))=100{,}000\). Expected annual recovery is:
Expected retained loss is \(25{,}000-10{,}000=15{,}000\). As a check, Event A leaves \(150{,}000-50{,}000=100{,}000\) retained, and Event B leaves \(200{,}000-100{,}000=100{,}000\); their weighted expected retained amount is \(0.10(100{,}000)+0.05(100{,}000)=15{,}000\). Common mistake avoided: applying reinsurance to ground-up damage rather than to the insurer’s policy payment as specified.
Reviewing a Model Output for Ratemaking
A model output should be reviewed in light of the purpose for which it will be used. For an expected-loss indication, the analyst should confirm that event weights and conditional losses are combined consistently, that losses are measured at the intended financial stage, and that the modeled portfolio matches the coverage being priced. An expected ground-up loss, an expected policy payment, and an expected retained loss are different quantities; the label on a report should make the distinction clear.
The model’s architecture also helps identify where judgment enters. Event generation represents frequency assumptions; hazard and vulnerability represent physical effects and damage relationships; exposure data represents the insured property; financial calculations represent contract terms. A change to any of these can change the result, but it changes it through a different mechanism. This separation is useful for sensitivity analysis and for explaining an indication to reviewers.
Confirm whether the figure is ground-up loss, policy payment, reinsurance recovery, or retained loss, and whether it is per event or annual.
Follow the assumed event occurrence, hazard output, exposure representation, and vulnerability conversion that produced the loss.
Check that policy and reinsurance terms are applied to the correct loss amount and at the correct aggregation level.
Compare the final indication with the intended ratemaking measure and avoid treating one expected-loss number as a complete description of risk.
Common Architecture Traps
- Confusing hazard, damage, and payment. Hazard is a physical event effect; vulnerability translates it into damage; financial terms determine contractual payments. These are successive stages, not interchangeable labels.
- Mixing aggregation levels. A deductible may apply by location or by event, while a reinsurance attachment may apply to an event aggregate. Applying terms at a different level can materially change the result.
- Using a frequency without its severity basis. A conditional mean loss must correspond to the same event definition and financial basis as the event rate used in the calculation.
- Comparing differently defined outputs. A ground-up result cannot be compared directly with a net-of-terms indication without accounting for the intervening financial calculations.
- Assuming an expected loss captures all pricing considerations. Expected loss is a central component of pricing, but it does not by itself describe variability or tail risk. A pricing indication may require additional considerations appropriate to the intended use.
Check Your Understanding
For each problem, trace the stated quantities through the relevant model stages and check that the final answer uses the requested loss basis.
- A hypothetical event type has an annual Poisson rate of 0.10 and a conditional mean ground-up event loss of $400,000. Under the stated frequency and severity assumptions, what is the expected annual ground-up loss? (Answer: $40,000.)
- A modeled event produces $120,000 of damage. A policy applies a $20,000 deductible and has a $70,000 payment limit. What is the insurer’s policy payment before reinsurance? (Answer: $70,000.)
- A hypothetical model has two event types. Type A has annual rate 0.20 and mean insurer event payment of $25,000; Type B has annual rate 0.10 and mean insurer event payment of $60,000. What is expected annual insurer payment? (Answer: $11,000.)
- Annual outcomes are mutually exclusive: no event with probability 0.80, a $100,000 ground-up loss with probability 0.15, and a $300,000 ground-up loss with probability 0.05. A policy applies a $25,000 deductible and a $150,000 payment limit. Find expected annual policy payment before reinsurance. (Answer: $18,750.)
- Two hypothetical event types have annual rates 0.10 and 0.05 and ground-up event losses of $100,000 and $300,000, respectively. A policy applies a $20,000 deductible and a $150,000 payment limit. The resulting policy payments are subject to $50,000 excess of $40,000 reinsurance. Find expected annual retained loss. (Answer: $9,000.)