How does scenario-based capital assessment work under AMA?

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AcadiFi · Accepted Answer

Under the Advanced Measurement Approach (AMA), scenario analysis outputs directly inform the operational VaR at 99.9% confidence over a one-year horizon...

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Mechanics: each scenario produces frequency (λ) — events per year — and severity points (x1, x2, x3) representing typical, expected-severe, and extreme outcomes. For a rogue-trader scenario at Apex Global Markets, frequency might be 1/25 years (0.04), typical severity $50 million, severe $200 million, extreme $1 billion.

Two common integration approaches: (1) scenarios as data points — each scenario becomes a synthetic loss observation fitted alongside internal and external loss data into a severity distribution (typically lognormal or generalized Pareto); (2) hybrid distributions — separate distributions for body (internal data), middle (external data), and tail (scenarios), spliced at defined thresholds.

```mermaid
flowchart TD
  A[Expert Scenarios] --> B[Freq + Severity]
  B --> C[Synthetic Loss Points]
  C --> D[Severity Distribution]
  D --> E[Monte Carlo]
  E --> F[99.9% OpVaR]
```

Monte Carlo simulation: draw the annual frequency from Poisson(λ), then draw that many severity values from the fitted distribution, sum to get annual loss. Repeat 100,000+ times to build the annual loss distribution, read the 99.9th percentile as OpVaR.

Capital impact: scenarios typically drive 40-60% of total OpVaR because they dominate the tail. A bank that revises its scenarios by increasing severity estimates 20% might see capital rise 8-12%. This creates a governance tension — risk managers want conservative scenarios to capture risk honestly, while business lines pressure for less conservative numbers to reduce capital. Independent challenge processes and third-party validation are required by regulators.

Post-2017 regulatory framework: the Standardized Measurement Approach (SMA) replaces AMA for most jurisdictions, computing capital from business indicators plus an internal loss multiplier. Scenarios still inform internal capital management and stress testing even where regulatory capital uses SMA formulas.

How does scenario-based capital assessment work under AMA?

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