CapeCod

CapeCod#

class chainladder.CapeCod(trend=0, decay=1, n_iters=1, apriori_sigma=0.0, random_state=None, groupby=None)[source]#

Applies the CapeCod technique to triangle X

Parameters:

trend: float, optional (default=0.0): The cape cod trend assumption. Any Trend transformer on X will override this argument.
decay: float, optional (default=1.0): The cape cod decay assumption. This parameter is required by the Generalized Cape Cod Method, as discussed in [Using Best Practices to Determine a Best Reserve Estimate](https://www.casact.org/sites/default/files/database/forum_98fforum_struhuss.pdf) by Struzzieri and Hussian. As the decay factor approaches 1 (the default value), the result approaches the traditional Cape Cod method. As the decay factor approaches 0, the result approaches the Chainladder method.
n_iters: int, optional (default=1): Number of iterations to use in the Benktander model.
groupby: str or list, optional (default=None): An option to group levels of the triangle index together for the purposes of deriving the apriori measures. If omitted, each level of the triangle index will receive its own apriori computation.
apriori_sigma: float, optional (default=0.0): Standard deviation of the apriori. When used in conjunction with the bootstrap model, the model samples aprioris from a lognormal distribution using this argument as a standard deviation.
random_state: int, RandomState instance or None, optional (default=None): Seed for sampling from the apriori distribution. This is ignored when using as a deterministic method. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.

Attributes:

triangle:: returns X
ultimate_:: The ultimate losses per the method
ibnr_:: The IBNR per the method
apriori_:: The trended apriori vector developed by the Cape Cod Method
detrended_apriori_:: The detrended apriori vector developed by the Cape Cod Method

Examples

Unlike Bornhuetter-Ferguson and Benktander, CapeCod derives the apriori loss ratio from the data itself. sample_weight represents exposure (e.g. earned premium) rather than an apriori expected ultimate.

xyz = cl.load_sample("xyz")

ibnr = (
    cl.CapeCod().fit(X=xyz["Paid"], sample_weight=xyz["Premium"].latest_diagonal).ibnr_
)
print(ibnr)

              2261
         NaN
   88.211299
  698.247374
 1858.151261
 4611.796594
10640.571396
25916.281295
53264.037933
56079.713590
40470.540502
35043.822927

With default decay=1 and trend=0, every origin receives the same apriori loss ratio: the exposure-weighted mean loss ratio across all origins.

apriori = (
    cl.CapeCod()
    .fit(X=xyz["Paid"], sample_weight=xyz["Premium"].latest_diagonal)
    .apriori_
)
print(apriori)

Setting decay below 1 down-weights distant origins when computing each origin’s apriori, so each origin receives its own loss-ratio estimate that drifts toward more recent experience.

apriori = cl.CapeCod(decay=0.5).fit(
    X=xyz["Paid"], sample_weight=xyz["Premium"].latest_diagonal
).apriori_
print(apriori)

Setting trend projects the loss ratio forward over the experience period.

apriori = (
    cl.CapeCod(decay=0.5, trend=0.03)
    .fit(X=xyz["Paid"], sample_weight=xyz["Premium"].latest_diagonal)
    .apriori_
)
print(apriori)

fit(X, y=None, sample_weight=None)[source]#

Fit the model with X.

Parameters:

X: Triangle-like: Loss data to which the model will be applied.
y: None: Ignored
sample_weight: Triangle-like: The exposure to be used in the method.
Returns
——-
self: object: Returns the instance itself.

Examples

Fit returns the estimator itself, with ultimate_ and apriori_ populated. The repr shows non-default parameters.

tr = cl.load_sample('ukmotor')
exposure = cl.Chainladder().fit(tr).ultimate_ * 0 + 20000
print(cl.CapeCod(trend=0.05).fit(tr, sample_weight=exposure))

predict(X, sample_weight=None)[source]#

Predicts the CapeCod ultimate on a new triangle X

Parameters:

X: Triangle: Loss data to which the model will be applied.
sample_weight: Triangle: For exposure-based methods, the exposure to be used for predictions

Returns:

X_new: Triangle: Loss data with CapeCod ultimate applied

Examples

Fit on a prior-period view of the data, then apply the model to the current Triangle and a refreshed exposure.

tr = cl.load_sample('ukmotor')
tr_prior = tr[tr.valuation < tr.valuation_date]
exposure_prior = cl.Chainladder().fit(tr_prior).ultimate_ * 0 + 20000
exposure = cl.Chainladder().fit(tr).ultimate_ * 0 + 20000
model = cl.CapeCod(trend=0.05).fit(
    tr_prior, sample_weight=exposure_prior
)
print(model.predict(tr, sample_weight=exposure).ultimate_)

              2261
12690.000000
12746.000000
13631.353487
12896.639975
13806.211939
15991.144199
17489.630279

Inherited Methods

`CapeCod.fit_predict`
`CapeCod.get_metadata_routing`	Get metadata routing of this object.
`CapeCod.get_params`	Get parameters for this estimator.
`CapeCod.intersection`	Given two Triangles with mismatched indices, this method aligns their indices
`CapeCod.pipe`
`CapeCod.set_backend`	Converts triangle array_backend.
`CapeCod.set_params`	Set the parameters of this estimator.
`CapeCod.to_json`	Serializes triangle object to json format
`CapeCod.to_pickle`	Serializes triangle object to pickle.
`CapeCod.validate_X`
`CapeCod.validate_weight`

CapeCod

Contents

CapeCod#