Value at Risk

import chainladder as cl

This example uses the BootstrapODPSample to simulate new triangles that are then used to simulate an IBNR distribution from which we can do Value at Risk percentile lookups.

# Load triangle
triangle = cl.load_sample('genins')

# Create 1000 bootstrap samples of the triangle
resampled_triangles = cl.BootstrapODPSample(random_state=42).fit_transform(triangle)

# Create 1000 IBNR estimates
sim_ibnr = cl.Chainladder().fit(resampled_triangles).ibnr_.sum('origin')

# X - mu
sim_ibnr = (sim_ibnr - sim_ibnr.mean()).to_frame().sort_values()

/home/docs/checkouts/readthedocs.org/user_builds/chainladder-python/envs/experimental/lib/python3.11/site-packages/chainladder/adjustments/bootstrap.py:284: UserWarning: 'where' used without 'out', expect unitialized memory in output. If this is intentional, use out=None.
  hat = xp.diagonal(xp.sqrt(xp.divide(1, abs(1 - hat), where=(1 - hat) != 0)))

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import matplotlib.pyplot as plt
plt.style.use('ggplot')
%config InlineBackend.figure_format = 'retina'

# Plot data
fig, ax = plt.subplots()
sim_ibnr.index = [item/1000 for item in range(1000)]
(sim_ibnr/1e6).loc[0.90:].plot(kind='area', alpha=0.5,
    title='Bootstrap VaR (90% and above)', ax=ax).set(
    xlabel='Percentile', xlim=(0.899, 1.0), ylabel='Value (Millions)');
ax.grid(axis='y')
for spine in ax.spines:
    ax.spines[spine].set_visible(False)