r"""
Basel historical VaR and the traffic light
==========================================

The 1996 Market Risk Amendment let banks set capital from their own
99%, ten-day VaR, typically historical simulation over at least a year
of data, multiplied by at least 3. The multiplier grows with the
number of exceptions in the last 250 days: green (0-4) keeps 3, yellow
(5-9) adds 0.40 to 0.85, red (10 or more) adds 1. Here a historical
VaR is run on a market whose volatility doubles halfway through.
"""

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

from financialkit.risk import basel_traffic_light, rolling_historical_var, var_exceptions
from financialkit.risk.visualizers import plot_backtest

# %%
# The zones
# ---------

for k in range(12):
    res = basel_traffic_light(k)
    print(f"{k:2d} exceptions: {res.zone:6s} P(X <= k) = {res.cumulative_probability:.4f}  multiplier {res.multiplier:.2f}")

# %%
# A one-year window behind a volatility jump
# ------------------------------------------

rng = np.random.default_rng(7)
vol = np.r_[np.full(750, 0.01), np.full(500, 0.02)]
pnl = vol * rng.standard_t(5, vol.size) / np.sqrt(5 / 3)
window = 250
var = rolling_historical_var(pnl, window, 0.99)
test = pnl[window:]
hits = var_exceptions(test, var)
plot_backtest(test, var)

counts = np.array([hits[t - 250 : t].sum() for t in range(250, hits.size + 1)])
zones = [basel_traffic_light(int(c)).zone for c in counts]
fig, ax = plt.subplots(figsize=(8, 3))
colors = {"green": "C2", "yellow": "C1", "red": "C3"}
ax.scatter(np.arange(counts.size) + 250, counts, c=[colors[z] for z in zones], s=4)
ax.set_xlabel("day of the backtest")
ax.set_ylabel("exceptions in last 250 days")
fig.tight_layout()

plt.show()