r"""
The ISDA standard model: bootstrapping hazard rates
===================================================

Since the 2009 "Big Bang" CDS trade with a fixed coupon (100 or 500 bp)
and an upfront payment, and the ISDA standard model converts between
quotes by bootstrapping a piecewise-constant hazard curve: solve for the
hazard on :math:`(0, T_1]` that reprices the shortest CDS, freeze it, solve
the next segment, and so on. The bootstrapped curve reprices every quote
and gives survival probabilities at any date.
"""

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

from financialkit.credit import bootstrap_hazard_curve, cds_par_spread, cds_upfront, upfront_to_spread
from financialkit.credit.visualizers import plot_survival

maturities = np.array([0.5, 1, 2, 3, 4, 5, 7, 10])
spreads = np.array([45, 55, 80, 105, 125, 140, 155, 165]) * 1e-4
r, R = 0.03, 0.4

curve = bootstrap_hazard_curve(maturities, spreads, r, R)
for T, s, h in zip(maturities, spreads, curve.hazards, strict=True):
    print(f"{T:4.1f}y  quote {1e4 * s:5.0f} bp  hazard {h:.4%}  reprices to {1e4 * cds_par_spread(curve, T, r, R):7.2f} bp")

# %%
# The curve
# ---------

fig, ax = plt.subplots(figsize=(7, 4))
plot_survival(curve, T=10.0, ax=ax, label="bootstrapped survival")
ax.legend(loc="lower left")

# %%
# Upfronts at the standard coupons
# --------------------------------
#
# With a 100 bp coupon the buyer pays upfront when the par spread is
# higher and receives it when lower; the conversion back to a
# flat-hazard "conventional" spread recovers roughly the quote.

up100 = [cds_upfront(curve, T, 0.01, r, R) for T in maturities]
up500 = [cds_upfront(curve, T, 0.05, r, R) for T in maturities]
conv = [upfront_to_spread(u, 0.01, T, r, R) for u, T in zip(up100, maturities, strict=True)]
fig, ax = plt.subplots(1, 2, figsize=(11, 4))
ax[0].bar(maturities - 0.15, 100 * np.array(up100), 0.3, label="coupon 100 bp")
ax[0].bar(maturities + 0.15, 100 * np.array(up500), 0.3, label="coupon 500 bp")
ax[0].axhline(0, color="k", lw=0.8)
ax[0].set_xlabel("maturity")
ax[0].set_ylabel("upfront (% of notional)")
ax[0].legend()
ax[1].plot(maturities, 1e4 * spreads, "o", label="par quote")
ax[1].plot(maturities, 1e4 * np.array(conv), "x-", label="conventional spread from upfront")
ax[1].set_xlabel("maturity")
ax[1].set_ylabel("bp")
ax[1].legend()

plt.show()