r"""
Boudoukh-Richardson-Whitelaw hybrid VaR
=======================================

Historical simulation gives every day in the window the same weight, so
after a jump in volatility it takes months to notice and then drops the
crisis days abruptly when they leave the window. Boudoukh, Richardson
and Whitelaw (1998) weighted the outcome :math:`i` days old by
:math:`\lambda^i`, combining RiskMetrics' exponential smoothing with
historical simulation's distribution-free tail: "the best of both worlds".
"""

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

from financialkit.risk import historical_var, hybrid_var
from financialkit.risk.visualizers import plot_var

rng = np.random.default_rng(11)
vol = np.r_[np.full(500, 0.008), np.full(150, 0.025), np.full(350, 0.008)]
pnl = vol * rng.standard_t(5, vol.size) / np.sqrt(5 / 3)
window = 250

# %%
# Rolling forecasts through a turbulent spell
# -------------------------------------------

days = np.arange(window, pnl.size)
hs = [historical_var(pnl[t - window : t], 0.99).var for t in days]
bw = [hybrid_var(pnl[t - window : t], 0.99, lam=0.98).var for t in days]
fig, ax = plt.subplots(figsize=(8, 3.8))
ax.plot(np.arange(pnl.size), pnl, color="0.75", lw=0.6)
ax.plot(days, -np.array(hs), label="historical (equal weights)")
ax.plot(days, -np.array(bw), label="hybrid, lambda = 0.98")
ax.plot(np.arange(pnl.size), -2.326 * vol, "k:", lw=1, label="true 99% normal-equivalent")
ax.set_xlabel("day")
ax.set_ylabel("P&L and minus VaR")
ax.legend(loc="lower left", fontsize=8)
fig.tight_layout()

# %%
# The weighted distribution on the first turbulent days
# -----------------------------------------------------
#
# Twenty days into the turbulent period the hybrid method already puts
# a third of its probability mass on them.

t = 520
res = hybrid_var(pnl[t - window : t], 0.99, 0.98)
print(f"weight on last 20 days: {res.weights[-20:].sum():.2f}  (equal weighting: {20 / window:.2f})")
plot_var(res)

plt.show()