Why Catastrophe-Model Output Governance Matters
A catastrophe model can produce a precise-looking loss estimate, but that estimate is only useful in ratemaking if another reviewer can determine which run produced it, what went into the run, and how the result became the selected ratemaking measure. Two analysts may use the same vendor model and still obtain different indicated losses because they used different exposure snapshots, financial terms, model settings, or transformations.
Output governance is the control of that chain of evidence. It does not mean treating a model result as automatically correct. It means preserving enough information to reproduce the result and identify where a discrepancy entered. This is aligned with the CAS Exam 8 (Advanced Ratemaking) syllabus, where modeled catastrophe losses may inform pricing and reinsurance decisions.
The Reproduction Record
A useful record makes a run identifiable and reproducible rather than merely describing it as “the latest vendor output.” At minimum, retain the following information or an explicit reference to the controlled record that contains it.
- Model identity: vendor, model name, release or version, applicable hazard module, and any enabled secondary modules.
- Run identity: unique run identifier, run date, software or platform version where relevant, and the person or process that initiated the run.
- Exposure inputs: the frozen input-file identifier, file hash or equivalent integrity check, valuation date, exposure count and totals, currency, and material field mappings or data treatments.
- Financial terms: the terms applied, their scope, and their order. Record whether deductibles and limits are per location, occurrence, or another defined basis, and whether a stated limit caps payment or total loss.
- Output definition: the output measure, peril and geography, units, currency, time basis, and whether the result is gross, insured, or otherwise net of specified terms.
- Transformations: each subsequent adjustment, including its formula, input and output units, source, and reason for use.
- Checks and approvals: reconciliation totals, exceptions, reviewer evidence, and the approved output file or table used in the indication.
These records complement the earlier material on reproducible ratemaking workflows, version control, assumption registers, and independent review. A model version alone is not a reproducible run: an exposure file or financial-term configuration can change while the model release stays fixed. Conversely, a changed output does not establish that a model changed; the cause might be an input or a transformation.
Keep the Loss Measures and Transformations Distinct
The term “modeled loss” is not sufficiently precise for an audit trail. A result may be a ground-up loss, a loss after specified contract terms, an annual average loss, or a transformed ratemaking amount. The record should name the measure and preserve intermediate results so a reviewer can distinguish model output from subsequent calculations.
For a finite event catalog, let event \(j\) have annual occurrence rate \(\lambda_j\) and insured loss \(Y_j\) after the stated financial terms. If event counts have expected values \(\lambda_j\), losses are additive, and there is no separate annual aggregate cap, the expected annual loss is
This is an expectation calculation: the expected contribution from event \(j\) is its expected count multiplied by its loss per occurrence. By linearity of expectation, the contributions add; independence between event types is not required for this sum. The expression does not, by itself, specify the distribution of annual aggregate loss, account for an annual aggregate limit, or define how the event rates were estimated. Those matters must not be silently inferred from an AAL.
Reproduce a Financial-Term Calculation
Financial terms can change the modeled amount materially, so they must be recorded in executable terms rather than with an ambiguous label such as “standard deductible.” The following example treats a limit as a cap on the insurer’s payment after the deductible. A different contract definition would produce a different result.
Worked Example: Rebuilding an Annual Average Loss After Terms
A hypothetical property portfolio has a three-event model catalog. Event A has annual rate \(0.020\) and portfolio ground-up loss of $700,000; Event B has annual rate \(0.010\) and loss of $1,300,000; Event C has annual rate \(0.005\) and loss of $2,400,000. Apply a $100,000 per-occurrence deductible and a $900,000 maximum insurer payment per occurrence. Calculate the annual average insured loss.
Method and assumptions. The catalog is a discrete set of event types with the stated annual occurrence rates and deterministic losses for this calculation. Expected annual event counts equal those rates. Losses are additive, there is no annual aggregate limit, and the occurrence deductible and payment cap apply once to each event’s portfolio loss. No interest discounting or mortality assumption is used; no probability distribution beyond the stated event-rate representation is assumed.
For ground-up event loss \(L_j\), the payment under these terms is \(Y_j=\min(\max(L_j-100{,}000,0),900{,}000)\). For Event A, the loss after the deductible is $700,000 − $100,000 = $600,000, below the payment cap, so \(Y_A=$600{,}000\).
For Event B, the amount after the deductible is $1,300,000 − $100,000 = $1,200,000. The payment cap applies, so \(Y_B=\min($1{,}200{,}000,$900{,}000)=$900{,}000\).
For Event C, the amount after the deductible is $2,400,000 − $100,000 = $2,300,000. The cap again applies, giving \(Y_C=$900{,}000\).
The annual average insured loss is therefore
The result is $25,500 per year. As a check, each event’s payment is nonnegative and no payment exceeds $900,000. A common mistake is to apply the $900,000 cap to the loss before the deductible, which would produce different payments. The stated contract interpretation requires subtracting the deductible first and then capping the insurer’s payment.
Carry the Result Through a Ratemaking Transformation
After a model output is produced, an analyst may transform it to a selected valuation basis or express it as a loss cost per unit of exposure. Such arithmetic can be straightforward, but undocumented units, misplaced factors, or changed denominators make the final figure difficult to reproduce. Keep the source result, adjustment factors, and denominator visible.
Worked Example: Reconciling Adjusted Loss Costs by Territory
A hypothetical catastrophe-model run reports annual average insured losses of $32,000 for Territory North and $54,000 for Territory South, both in current dollars and after the specified contract terms. The ratemaking analysis applies a documented common trend factor of 1.05. Insured values are $40,000,000 and $60,000,000, respectively. Calculate adjusted loss costs per $1,000 of insured value by territory and for the portfolio.
Method and assumptions. Treat the reported AALs as fixed model statistics; no underlying probability distribution is provided or inferred. The trend factor is applied once to each territory’s AAL. There is no interest discounting or mortality assumption. The exposure denominator is insured value in dollars, and no other load or adjustment is included.
North’s adjusted AAL is $32,000 × 1.05 = $33,600. Its exposure is $40,000,000 ÷ $1,000 = 40,000 units of $1,000. Thus, its adjusted loss cost is $33,600 ÷ 40,000 = $0.84 per $1,000.
South’s adjusted AAL is $54,000 × 1.05 = $56,700. Its exposure is $60,000,000 ÷ $1,000 = 60,000 units of $1,000. Its adjusted loss cost is $56,700 ÷ 60,000 = $0.945 per $1,000.
The portfolio adjusted AAL is $33,600 + $56,700 = $90,300. Total insured value is $40,000,000 + $60,000,000 = $100,000,000, or 100,000 units of $1,000. The portfolio loss cost is $90,300 ÷ 100,000 = $0.903 per $1,000.
As a check, the portfolio result is the exposure-weighted average: \((40{,}000\times\$0.84+60{,}000\times\$0.945)/100{,}000=\$0.903\). Reported to the nearest cent, the territory amounts are $0.84 and $0.95 per $1,000, and the portfolio amount is $0.90 per $1,000. Rounding is only at the final step; retaining the unrounded South amount is necessary for the portfolio reconciliation. A common mistake is to average the two territory rates equally, ignoring their different exposure volumes.
Find and Explain a Unit-Reconciliation Failure
A reproducible calculation needs more than a final total: it should expose unit conversions and intermediate values. This is especially important when a vendor export uses thousands of dollars while a financial-term file uses dollars. A unit label is part of the input, not a display detail.
Worked Example: Detecting a Thousands-of-Dollars Error
A hypothetical model export gives ground-up event losses in thousands of dollars: Event P is 250, Event Q is 80, and Event R is 500. Their annual rates are \(0.040\), \(0.020\), and \(0.010\). Apply a $100,000 per-occurrence deductible and a $300,000 maximum insurer payment per occurrence, where the limit caps payment after the deductible. Calculate the insured AAL.
Method and assumptions. The three stated event types form a discrete event catalog; their annual rates are expected annual counts, event losses are deterministic, and there is no annual aggregate limit. Convert the export to dollars before applying the dollar-denominated terms. No interest discounting or mortality assumption is used, and no distribution beyond the supplied rates and event losses is assumed.
First convert each loss: P is 250 × $1,000 = $250,000; Q is 80 × $1,000 = $80,000; and R is 500 × $1,000 = $500,000.
P’s amount after the deductible is $250,000 − $100,000 = $150,000, below the cap, so its payment is $150,000. Q is below the deductible, so its payment is $0. R’s amount after the deductible is $500,000 − $100,000 = $400,000, which is capped at $300,000.
The insured AAL is \((0.040)(\$150{,}000)+(0.020)(\$0)+(0.010)(\$300{,}000)=\$6{,}000+\$0+\$3{,}000=\$9{,}000\). Thus the result is $9,000 per year. The check is that the unit conversion occurs before comparison with the dollar deductible: Event Q’s $80,000 loss is below $100,000. A common mistake is to compare the raw number 80 directly with $100,000, mixing thousands of dollars and dollars, or to apply terms before converting. The run record should retain the export unit, conversion, term unit, and converted event amounts.
Practical Controls for a Traceable Output
A reviewer should be able to move from the selected ratemaking value back through the transformations to the exact model run and its inputs. A concise control sequence helps make that review systematic.
Record the model release, run identifier, date, peril scope, settings, and controlled output-file location.
Reference the exact exposure snapshot and record its integrity check, valuation date, units, key totals, and material data mappings.
Document the scope and order of deductibles, limits, and other terms, including the interpretation of each limit.
Name the original loss measure and record each adjustment, conversion, aggregation, or denominator calculation separately.
Check totals and units, investigate exceptions, retain the final calculation, and link reviewer evidence to the selected result.
A frequent governance failure is storing a final rate indication without preserving its lineage. Another is retaining a vendor report but not the exposure snapshot or configuration needed to reproduce it. In either case, a reviewer may be unable to distinguish a changed model output from a changed input, financial term, or post-model adjustment. The remedy is not simply more documentation: it is a record organized around the calculation’s actual dependencies, with each result tied to the versioned inputs and explicit operations that produced it.
Check Your Understanding
For each problem, identify the relevant output or control and check your arithmetic before consulting the answer.
- A hypothetical run uses a model release identified as R7 and an exposure file with 12,400 locations. The final report has no exposure-file hash or valuation date. Name two missing items needed to identify and reproduce the input snapshot. (Answer: An integrity identifier such as a file hash and the exposure valuation date.)
- A discrete event catalog has Event M with annual rate \(0.015\) and insured loss $400,000, and Event N with annual rate \(0.005\) and insured loss $1,000,000. Assuming additive losses and no annual aggregate cap, calculate AAL. (Answer: \(0.015\times\$400{,}000+0.005\times\$1{,}000{,}000=\$11{,}000\) per year.)
- A model reports fixed AALs of $24,000 and $36,000 for two territories. Apply a common factor of 1.10. Their insured values are $30,000,000 and $70,000,000. Calculate the portfolio adjusted loss cost per $1,000 of insured value. (Answer: Adjusted AAL is $66,000; total exposure is 100,000 units of $1,000; loss cost is $0.66 per $1,000.)
- An event has ground-up loss $750,000, a $50,000 per-occurrence deductible, and a $500,000 payment cap after the deductible. Its annual rate is \(0.020\). What is its AAL contribution? (Answer: Payment is \(\min(\$750{,}000-\$50{,}000,\$500{,}000)=\$500{,}000\); contribution is $10,000 per year.)
- A report states that portfolio AAL is $84,000 after a trend factor of 1.05, but the source AAL and transformation sequence are absent. If the factor was applied once to the source AAL, what source amount would reconcile, and what must be documented to verify it? (Answer: Source AAL is \(\$84{,}000/1.05=\$80{,}000\); document the exact source run and output, factor value and rationale, units, application formula, and reconciliation.)