Runtime Frequency

Runtime (Frequency)

This page explains common frequency models used in CRML scenarios.

CRML frequency is expressed as a rate model plus a basis:

• scenario.frequency.model: a model identifier (engine-defined support)
• scenario.frequency.basis: portable semantic meaning of the rate unit

See: CRML Specification (Overview)

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Basis semantics (portable)

Two basis values are standardized by the language:

• per_organization_per_year: the scenario’s frequency already represents the total org-wide annual rate.
• per_asset_unit_per_year: the scenario’s frequency represents a per-unit annual rate and MUST be scaled by bound exposure $E$.

For the normative definition of $E$ (how portfolios bind scenarios to assets), see Exposure scaling and frequency basis.

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Common models

Poisson

A Poisson process is often used for independent event counts.

If the annual rate is $\lambda$, then the event count $N$ in a year is:

$$ N \sim \text{Poisson}(\lambda) $$

For per_asset_unit_per_year, the effective annual rate becomes:

$$ \lambda_{\text{total}} = \lambda \cdot E $$

Gamma–Poisson (negative binomial)

A common way to model over-dispersion is to treat the Poisson rate as random:

$$ \lambda \sim \text{Gamma}(k, \theta), \quad N \mid \lambda \sim \text{Poisson}(\lambda) $$

The resulting marginal distribution for $N$ is negative binomial-like (engine parameterization may vary).

Hierarchical Gamma–Poisson

A hierarchical extension can model uncertainty in rate parameters across similar organizations or units. Details are engine-defined.

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Reference engine status

Implemented frequency models in the reference engine are listed here:

• Engine capabilities: Supported models