r"""
Geske compound options
======================

Robert Geske (1979) priced an option on an option. His motivation was
corporate finance: if equity is a call on the firm's assets, a stock
option is a call on a call, and its implied volatility should rise as
the stock falls and leverage grows. The compound call is exercised at
:math:`T_1` only if the underlying option is worth more than the
compound strike, which happens above a critical spot :math:`I`, and the
joint law of the price at :math:`T_1` and :math:`T_2` brings in the
bivariate normal distribution with correlation :math:`\sqrt{T_1/T_2}`.
"""

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

from financialkit.exotic_options import compound_option_price, critical_price
from financialkit.options import black_scholes_price

K1, K2, T1, T2, r, sigma = 5.0, 100.0, 0.25, 1.0, 0.05, 0.3
S = np.linspace(60.0, 150.0, 200)
print(f"Haug (2007), 4.6, put on call: {compound_option_price(500.0, 50.0, 520.0, 0.25, 0.5, 0.08, 0.35, q=0.03, option_type='put'):.4f}")

# %%
# The four compound options
# -------------------------

fig, axes = plt.subplots(1, 2, figsize=(12, 4))
for underlying in ("call", "put"):
    I = critical_price(K1, K2, T2 - T1, r, sigma, underlying_type=underlying)
    for option_type in ("call", "put"):
        axes[0].plot(
            S, compound_option_price(S, K1, K2, T1, T2, r, sigma, option_type=option_type, underlying_type=underlying), label=f"{option_type} on {underlying}"
        )
    axes[0].axvline(I, color="C0" if underlying == "call" else "C2", ls=":", lw=1)
axes[0].set_xlabel("spot S (dotted: critical spots I)")
axes[0].set_ylabel("value")
axes[0].legend()

# %%
# Compound put-call parity
# ------------------------
# Call on call minus put on call is the call minus the discounted
# compound strike, whatever the spot.

cc = compound_option_price(S, K1, K2, T1, T2, r, sigma)
pc = compound_option_price(S, K1, K2, T1, T2, r, sigma, option_type="put")
axes[1].plot(S, cc - pc, lw=3, label="call on call - put on call")
axes[1].plot(S, black_scholes_price(S, K2, T2, r, sigma) - K1 * np.exp(-r * T1), "k--", label=r"$c(S) - K_1 e^{-rT_1}$")
axes[1].set_xlabel("spot S")
axes[1].legend()
fig.tight_layout()
plt.show()