r"""
CreditRisk+ and Panjer's recursion
==================================

Credit Suisse First Boston's CreditRisk+ (1997) treated defaults like
insurance claims: Poisson events with rates driven by a gamma-distributed
sector factor, and exposures rounded to multiples of a loss unit. The
default count is then negative binomial, and Panjer's (1981) recursion
produces the whole loss distribution exactly, without simulation. The
factor's volatility :math:`\sigma` fattens the tail without changing the
expected loss.
"""

# %%
import matplotlib.pyplot as plt
import numpy as np

from financialkit.credit import creditrisk_plus
from financialkit.credit.visualizers import plot_loss_distribution

rng = np.random.default_rng(0)
exposures = np.round(rng.lognormal(np.log(2e5), 0.9, 300), -4)
pds = np.clip(rng.lognormal(np.log(0.01), 0.8, 300), 1e-4, 0.2)
unit = 50_000.0

fig, ax = plt.subplots(1, 2, figsize=(12, 4))
for a, sigma in zip(ax, (0.0, 1.0), strict=True):
    dist = creditrisk_plus(exposures, pds, sigma=sigma, unit=unit)
    plot_loss_distribution(dist, alpha=0.999, ax=a, log=True)
    a.set_title(f"sector volatility sigma = {sigma}")
    a.set_xlim(0, 2.5e7)
    a.set_ylim(1e-8, 1)
    print(f"sigma = {sigma}: EL {dist.mean:,.0f}, sd {dist.std:,.0f}, 99.9% UL {dist.unexpected_loss(0.999):,.0f}")

# %%
# Tail probabilities
# ------------------

fig, ax = plt.subplots(figsize=(7, 4))
for sigma in (0.0, 0.5, 1.0, 1.5):
    d = creditrisk_plus(exposures, pds, sigma=sigma, unit=unit)
    ax.semilogy(d.losses, 1 - np.cumsum(d.pmf), label=f"sigma = {sigma}")
ax.set_xlim(0, 3e7)
ax.set_ylim(1e-6, 1)
ax.set_xlabel("loss")
ax.set_ylabel("P(loss > x)")
ax.legend()

plt.show()