Designing Scenarios for Capital Model Use

Why Scenario Design Begins With a Narrative

A capital model can calculate an outcome only after a scenario has been translated into changes the model can use. A sentence such as “a severe storm disrupts the portfolio” is not yet a model input: it does not specify which exposures are affected, how the event changes claims, or what financial measure is to be reported. Scenario design connects a plausible cause to explicit model drivers and then to a quantified result.

A useful scenario is internally consistent: its drivers follow from the same narrative, apply to the stated model boundary and horizon, and do not count the same effect twice. The result is conditional on the assumptions specified. Unless a probability model is added and supported, it is not a forecast, a tail quantile, or an economic-capital estimate. The discipline of turning a scenario into a traceable model calculation is aligned with the CAS Exam 9 (Risk Management for Actuaries) syllabus.

Definition: A capital-model scenario is a defined set of conditional circumstances, expressed through changes to relevant model drivers, used to calculate an outcome on a stated loss or financial-position basis over a stated horizon. A scenario has a baseline for comparison, a causal narrative, specified assumptions, and a documented model translation.

The earlier material on model purpose, boundary, exposure units, loss basis, and risk inventory determines what the scenario calculation is intended to cover. Scenario design does not replace those choices. It uses them: the narrative must apply to the modeled perimeter, and the reported outcome must use the same measurement basis as the baseline.

From Narrative to Model Drivers

Start with a cause-and-effect chain. Identify the initiating event, the exposures or processes it affects, and the model quantities that change as a result. Then state which quantities are held fixed. This makes it possible to distinguish a scenario assumption from a model calculation and to identify missing links before running the model.

Define the scenario and boundary.
State the event, affected portfolio or process, measurement horizon, and modeled outcome. Avoid implying that exposures outside the boundary have been included.

Write the causal narrative.
Describe how the event affects claims, assets, expenses, or other drivers. Include a causal link for each material change rather than listing unrelated adverse movements.

Map causes to model inputs.
For every changed driver, record its baseline value, scenario value, unit, direction, and source or rationale. Identify inputs held constant.

Calculate and reconcile.
Run or reproduce the model calculation, compare the scenario result with the baseline on the same basis, and check that component impacts reconcile to the total change.

Communicate limitations and precision.
Separate assumed inputs from calculated outputs. State material exclusions and round results consistently with the quality of the inputs.

A driver map makes the translation reviewable. For example, a storm narrative might map to affected exposure count, claim frequency, average claim severity, and possibly claim-handling expense. If the modeled output is gross claim cost, a reinsurance recovery is outside that output; it must not be silently deducted. If the output is net cost, the applicable recovery calculation and its assumptions must be included explicitly.

Quantifying Joint Driver Changes

When a scenario changes more than one driver, calculate the scenario outcome from the scenario values, not by adding isolated percentage changes without checking for interaction. For a simple model with claim count $N$ and average claim severity $S$, aggregate claim cost is $C=NS$. This model assumes the stated count and severity refer to the same portfolio, horizon, and loss basis; it omits expenses, reinsurance, and other claim-cost components unless they are separately modeled.

C_0=N_0S_0,\qquad C_1=N_1S_1,\qquad \Delta C=C_1-C_0

Write $N_1=N_0+\Delta N$ and $S_1=S_0+\Delta S$. Substituting these into the scenario calculation gives:

\begin{aligned} \Delta C &=(N_0+\Delta N)(S_0+\Delta S)-N_0S_0\\ &=S_0\Delta N+N_0\Delta S+\Delta N\Delta S. \end{aligned}

The first two terms are the count and severity changes measured at baseline values. The final term is their interaction: the added claims also have the changed severity. This derivation follows directly by expanding the product and subtracting the baseline. It shows why simply adding the two baseline-based effects can understate the total when both drivers change in the same scenario. For a more complex model, the same principle applies: calculate the full scenario output using all scenario inputs, and reconcile rather than assuming the components are additive.

Worked Example: A Storm Changes Claim Count and Severity

A hypothetical commercial property portfolio is modeled for a one-year horizon on a gross incurred-claim-cost basis. In the baseline, the model uses 100 claims and an average severity of $200,000. A storm narrative supports a conditional scenario of 110 claims and average severity of $210,000, reflecting both additional affected properties and higher repair costs. Calculate the baseline cost, scenario cost, and change.

Method and assumptions. Use $C=NS$, with count multiplied by average severity. The scenario values are conditional model inputs, not a probability distribution. No interest rate or mortality assumption applies to this claim-cost calculation. Claim expenses and reinsurance recoveries are excluded, and all amounts are in dollars.

Baseline. The baseline cost is:

C_0=100\times \$200{,}000=\$20{,}000{,}000.

Scenario. Apply both scenario drivers together:

C_1=110\times \$210{,}000=\$23{,}100{,}000.

Change and check. The scenario increase is $C_1-C_0=\$23{,}100{,}000-\$20{,}000{,}000=\$3{,}100{,}000$. The decomposition gives $10\times \$200{,}000=\$2{,}000{,}000$ from the count change, $100\times \$10{,}000=\$1{,}000{,}000$ from severity, and $10\times \$10{,}000=\$100{,}000$ from the interaction. Their sum is $3,100,000, matching the direct calculation. Reported to the nearest $0.1 million, the change is $3.1 million.

Common mistake avoided. Adding only the two baseline-based effects gives $3.0 million and misses the $0.1 million interaction. The full scenario calculation includes the changed severity on the additional claims.

Worked Scenarios With Explicit Assumptions

The next examples illustrate two other kinds of translation: an operational claims-development narrative and a balance-sheet scenario. The calculation method depends on the chosen output. A scenario may report a change in claim cost, or a change in assets less liabilities; those are different measures and should not be blended.

Worked Example: Claims Inflation and Reopened Claims

A hypothetical liability portfolio has 40 open claims with a baseline estimated unpaid cost of $500,000 per claim, for a total of $20 million. For a one-year scenario, higher medical costs increase the estimate for each of the 40 claims by 5%. Separately, the narrative assumes that two previously closed claims reopen, each adding $300,000 of unpaid cost. Calculate the scenario total and its change from baseline.

Method and assumptions. The inflation adjustment applies only to the 40 open claims. The two reopened claims are additional and are not included in those 40; this avoids double counting. Costs are on the same unpaid-claim basis and horizon. The calculation is deterministic conditional on the stated assumptions: no probability distribution, interest rate, or mortality assumption is used.

Baseline. The baseline unpaid cost is $40\times \$500{,}000=\$20{,}000{,}000$.

Inflated open claims. The scenario cost per open claim is $\$500{,}000\times 1.05=\$525{,}000$. For 40 claims, this is $40\times \$525{,}000=\$21{,}000{,}000$, an increase of $1,000,000 over the open-claim baseline.

Reopened claims. Their additional cost is $2\times \$300{,}000=\$600{,}000$. Therefore the scenario total is $\$21{,}000{,}000+\$600{,}000=\$21{,}600{,}000$, and the increase from baseline is $\$21{,}600{,}000-\$20{,}000{,}000=\$1{,}600{,}000$. The components reconcile: $1,000,000 plus $600,000 equals $1,600,000. To the nearest $0.1 million, the increase is $1.6 million.

Common mistake avoided. Applying the 5% increase to the reopened-claim amount as well would contradict the stated narrative. The inflation assumption applies to the 40 open claims only; the reopened claims have their own specified cost.

Worked Example: Translating Asset and Liability Changes Into Net Position

A hypothetical insurer reports baseline assets of $120 million and liabilities of $130 million. A one-year market and claims scenario produces a $3 million asset loss and a $4 million liability increase. Calculate the baseline and scenario net positions, then state the signed change and the magnitude of deterioration.

Method and assumptions. Define net position as assets minus liabilities. The stated $3 million asset loss and $4 million liability increase are scenario model outputs, in millions of dollars, on the same valuation basis as the baseline. For this example, the liability valuation holds the effective annual interest rate at 3.0%; no mortality assumption is used. No probability distribution is assigned to the conditional scenario.

Baseline net position. Assets less liabilities give $120-130=-10$, so the baseline net position is $-\$10$ million.

Scenario values. Scenario assets are $\$120-\$3=\$117$ million. Scenario liabilities are $\$130+\$4=\$134$ million. The scenario net position is therefore $\$117-\$134=-\$17$ million.

Signed change and check. The signed change is scenario net position minus baseline net position: $-\$17\text{ million}-(-\$10\text{ million})=-\$7\text{ million}$. Thus the change in net position is $-\$7$ million, so the deterioration has a magnitude of $7 million. That magnitude equals the $4 million liability increase plus the $3 million asset loss. To the nearest $0.1 million, the signed change is $-\$7.0$ million and the deterioration magnitude is $7.0 million.

Common mistake avoided. Do not say that the signed change of $-\$7$ million equals the positive $7 million sum of the asset loss and liability increase. The signed change is negative; the deterioration’s magnitude is positive.

Documentation, Precision, and Review

A scenario result is only as interpretable as its documentation. Record the narrative and its translation together so a reviewer can follow the path from cause to outcome. At a minimum, the record should distinguish:

Scenario facts and assumptions: what is specified by the narrative, what is imposed as a modeling assumption, and what is held constant.
Driver mapping: each affected model input, its baseline and scenario values, unit, direction, and rationale.
Calculation basis: the model boundary, horizon, gross or net treatment, valuation basis, and the output being reported.
Limitations: material omissions, dependencies the model does not capture, and any uncertainty in the assumed values.
Precision: rounding appropriate to the quality of the inputs, without suggesting that conditional assumptions are measured more accurately than they are.

A scenario can be coherent without being assigned a probability. If probabilities are not estimated, do not describe the outcome as having a particular likelihood or as a percentile of a loss distribution. Similarly, a precisely calculated output does not make the scenario assumptions precise. For example, multiplying a rounded claim count by a rounded severity may produce an exact-looking dollar figure, but the meaningful reporting precision may be millions or tenths of a million.

A final review should challenge the causal chain and the arithmetic separately. Ask whether each driver change follows from the narrative, whether two inputs represent the same effect, and whether an effect has been omitted from the chosen output. Then recalculate the scenario from its inputs and verify that reported component changes reconcile to the total. A scenario that cannot pass these checks is not ready to support a capital-model conclusion.

Key takeaway: A well-designed scenario is a traceable conditional calculation: a clear narrative maps to defined model drivers, the complete scenario is evaluated on a stated basis, and the result is reported with assumptions, limitations, and precision made explicit.

Check Your Understanding

For each problem, calculate on the stated basis and distinguish the scenario result from any unstated probability claim.

A hypothetical portfolio has 80 claims at an average severity of $150,000. A one-year scenario changes these to 86 claims and $160,000 average severity. Calculate the baseline cost, scenario cost, and increase. (Answer: Baseline $12.00 million; scenario $13.76 million; increase $1.76 million.)
A portfolio’s baseline unpaid estimate is 25 claims at $400,000 each. A scenario raises the estimate for those claims by 4% and adds three reopened claims at $200,000 each, not subject to the 4% increase. Find the scenario total and change. (Answer: Scenario $11.00 million; increase $1.00 million.)
A hypothetical balance sheet has assets of $80 million and liabilities of $74 million. In a scenario, assets fall by 8% and liabilities rise by 2.5%. Calculate the scenario net position and its signed change from baseline. (Answer: Scenario assets $73.60 million; liabilities $75.85 million; net position $-\$2.25$ million; signed change $-\$8.25$ million.)
Baseline claim cost is 120 claims at $250,000 each. A scenario increases claim count by 10% and average severity by 8%. Calculate the total increase, including the interaction, and verify it against the direct scenario calculation. (Answer: Baseline $30.00 million; scenario $35.64 million; increase $5.64 million.)
A hypothetical reserve is $60 million. In a scenario, 3% inflation applies to this reserve and two separately identified reopened claims add $600,000 each; the reopened claims are not included in the reserve or subject to the 3% adjustment. Calculate the scenario reserve and change. (Answer: Scenario $63.00 million; increase $3.00 million.)

What You'll Learn