CapeCod Onleveling

import chainladder as cl
import pandas as pd

This example demonstrates how to incorporate on-leveling into the CapeCod estimator. The on-level approach emulates the approach taken by Friedland in “Estimating Unpaid Claims Using Basic Techniques” Chapter 10. The ParallelogramOLF estimator is new in chainladder 0.7.9 as is the xyz triangle.

# Grab a triangle
xyz = cl.load_sample("xyz")

# Premium on-leveling factors
rate_history = pd.DataFrame({
    "date": [
        "1/1/1999",
        "1/1/2000",
        "1/1/2001",
        "1/1/2002",
        "1/1/2003",
        "1/1/2004",
        "1/1/2005",
        "1/1/2006",
        "1/1/2007",
        "1/1/2008",
    ],
    "rate_change": [0.02, 0.02, 0.02, 0.02, 0.05, 0.075, 0.15, 0.1, -0.2, -0.2],
})

# Loss on-leveling factors
tort_reform = pd.DataFrame({
    "date": ["1/1/2006", "1/1/2007"],
    "rate_change": [-0.1067, -0.25],
})

# In addition to development, include onlevel estimator in pipeline for loss
pipe = cl.Pipeline(
    steps=[
        (
            "olf",
            cl.ParallelogramOLF(
                tort_reform,
                change_col="rate_change",
                date_col="date",
                vertical_line=True,
            ),
        ),
        ("dev", cl.Development(n_periods=2)),
        ("model", cl.CapeCod(trend=0.034)),
    ]
)

# Define X
X = cl.load_sample("xyz")["Incurred"]

# Separately apply on-level factors for premium
sample_weight = cl.ParallelogramOLF(
    rate_history, change_col="rate_change", date_col="date", vertical_line=True
).fit_transform(xyz["Premium"].latest_diagonal)

#  Fit Cod Estimator
pipe.fit(X, sample_weight=sample_weight)

# Create a Cape Cod pipeline without onleveling
pipe2 = cl.Pipeline(
    steps=[("dev", cl.Development(n_periods=2)), ("model", cl.CapeCod(trend=0.034))]
)

# Finally fit Cod Estimator without on-leveling
pipe2.fit(X, sample_weight=xyz["Premium"].latest_diagonal)

# Plot results
results = cl.concat(
    (
        pipe.named_steps.model.ultimate_.rename("columns", ["With On-level"]),
        pipe2.named_steps.model.ultimate_.rename("columns", ["Without On-level"]),
    ),
    1,
).T

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import matplotlib.pyplot as plt

plt.style.use("ggplot")
%config InlineBackend.figure_format = 'retina'

ax = results.plot(
    kind="bar", title="Cape Cod sensitivity to on-leveling", subplots=True, legend=False
);