Generalized Cape Cod Model (`TraditionalGCC`)¶

The Cape Cod method is a popoular deterministic method for forecasting ultimate losses use by actuaries when estimating loss reserves. Our Generalized Cape Cod model is based on the Cape Cod method, which assumes that the latent loss ratio for a given accident period is taken to be a weighted mean of all other loss ratios (both past and future). The weight is determined by earned premium volume, leverage on ATA factors, and temporal distance from accident period in question. Our TraditionalGCC model type implements the model, which is expressed mathematically as:

\[\begin{split}\begin{align*} \widehat{\mathrm{LR}}_i &= \frac{\sum_{k=1}^N \mathrm{LR}_k \cdot \mathrm{UEP}_k \cdot \beta^{\lvert k - i\rvert}}{\sum_{k=1}^N \mathrm{UEP}_k \cdot \beta^{\lvert k - i\rvert}}\\ \mathrm{UEP}_i &= \mathrm{EP}_i \frac{\mathrm{LR}_{\text{obs},i}}{\mathrm{LR}_{i}}\\ \beta &= \text{user input} \in (0, 1] \end{align*}\end{split}\]

where \(\widehat{\mathbf{LR}}\) is the model predicted loss ratio, \(\mathrm{LR}_i\) is the estimated ultimate loss ratio for each accident period \(i\) (which serves as input to the model), \(\mathrm{LR}_{\text{obs},i}\) is the latest observed loss ratio for accident period \(i\), and \(\mathrm{UEP}_i\) is the used earned premium for accident period \(i\). The used earned premium is calculated as the earned premium for the accident period multiplied by the ratio of observed to estimated ultimate losses. Therefore, used earned premium is lower for more recent accident periods.

The recency decay parameter \(\beta\) is a user-specified parameter that determines how steeply decay should occur across accident periods. A value of \(\beta = 1\) indicates no decay such that the predicted losses are simply the average of all accident period loss ratios. A value close to \(\beta \approx 0\) will put all the weight on the most recent accident period.

Model Fit Configuration¶

The TraditionalGCC model is fit using the following API call:

model = client.forecast_model.create(
    triangle=...,
    name="example_name",
    model_type="TraditionalGCC",
    config={ # default model_config
        "loss_definition": "incurred",
        "recency_decay": 0.9, # beta parameter above
    }
)

The TraditionalGCC model accepts the following configuration parameters in config:

loss_definition: Name of loss field to model in the underlying triangle (e.g., "reported", "paid", or "incurred"). Defaults to "incurred".
recency_decay: For the TraditionalGCC model, recency_decay corresponds directly to the \(\beta\) parameter in the mathematical expression above. Defaults to 0.9, which indicates that periods 1 year away get 90% weight, periods two years away would get 81% weight, and so forth.

Model Predict Configuration¶

The TraditionalGCC model is used to predict future losses using the following API call:

predictions = model.forecast_model.predict(
    triangle=...,
    config={}, # no extra config options
    target_triangle=None,
)

Above, triangle is the triangle to use to start making predictions from and target_triangle is the triangle to make predictions on. For most use-cases, triangle will be the same triangle that was used in model fitting, and target_triangle should be specified to include future accident periods (including earned premium values) that forecasts should be made on.

Generalized Cape Cod Model (TraditionalGCC)¶

Model Fit Configuration¶

Model Predict Configuration¶

Generalized Cape Cod Model (`TraditionalGCC`)¶