Runtime (Frequency)

This page explains common frequency models used in CRML scenarios.

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

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.

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:

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

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).

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

Implemented frequency models in the reference engine are listed here: