Option Pricing

# Para cada dia historico:
# 1. Obtener IV actual (e.g. de yahoo-finance) y precio de mercado
# 2. Calcular precio teorico con IV_historica
# 3. Comparar contra precio de mercado

# Precio teorico con IV_historica
py scripts/option_pricing.py bs --S 580 --K 580 --T 0.08 --r 0.05 --sigma 0.18
# -> 12.34

# Precio teorico con IV_actual (subestimada por el mercado)
py scripts/option_pricing.py bs --S 580 --K 580 --T 0.08 --r 0.05 --sigma 0.22
# -> 15.67

# P&L esperado = (market - teorico) = 15.67 - 12.34 = +3.33 (long vol paga)

# Para cada strike/expiry:
py scripts/option_pricing.py iv --S 580 --K 590 --T 0.08 --r 0.05 --price 8.50
# -> 0.2145 (la IV implicita de esa opcion)

py scripts/option_pricing.py greeks --S 580 --K 580 --T 0.08 --r 0.05 --sigma 0.20 --json
# Devuelve {delta: 0.512, gamma: 0.018, vega: 0.85, theta: -0.12, rho: 0.31}
# Comprar 1000 opc + short 512 acciones = delta neutral

# Opcion sobre indice con yield alto (e.g. SPX con div yield ~1.5%)
py scripts/option_pricing.py bs2 --S 5800 --K 5800 --T 0.25 --r 0.05 --q 0.015 \
  --sigma 0.18 --type call --style american
# -> ~123.45 (vs BS europea ~120.10, premium de early exercise = $3.35)

# Ejemplo 1: American put (Hull 21.1)
py scripts/option_pricing.py all --S 50 --K 50 --T 0.4167 --r 0.10 --sigma 0.40 \
  --type put --style american
# Output (9 rows: BS, Binomial, Trinomial, MC, LSM, BS2, P(ITM), P(Profit), Greeks):
# +---------------------------+------------------+-----------------------+
# | Method                    | Config           | Price / Value         |
# +---------------------------+------------------+-----------------------+
# | Black-Scholes             | closed-form O(1) | 4.076101              | (europea ref)
# | Binomial CRR              | N=500            | 4.283160              |
# | Trinomial                 | N=500            | 4.283429              |
# | Monte Carlo               | paths=100000     | 4.077892 +/- 0.0254   | (europea)
# | Longstaff-Schwartz        | paths=100000     | 4.258337              |
# | BS2/BAW (closed-form)     | O(1)             | 4.283766              |
# | P(ITM)                    | N(d2) bajo Q     | 0.4871                |
# | P(Profit) vs BS price     | premio=4.0761    | 0.3588                |
# | Greeks (delta/gamma/vega) | BS closed-form   | d=-0.3857 g=+0.0296   |
# +---------------------------+------------------+-----------------------+

# Ejemplo 2: European call (incluye Heston y Bates, NO incluye LSM/BS2)
py scripts/option_pricing.py all --S 100 --K 100 --T 0.25 --r 0.05 --sigma 0.20
# Output (9 rows: BS, Binomial, Trinomial, MC, Heston, Bates, P(ITM), P(Profit), Greeks):
# +---------------------------+----------------------------------------+-----------------------+
# | Method                    | Config                                 | Price / Value         |
# +---------------------------+----------------------------------------+-----------------------+
# | Black-Scholes             | closed-form O(1)                       | 4.614997              |
# | Binomial CRR              | N=500                                  | 4.613001              |
# | Trinomial                 | N=500                                  | 4.613999              |
# | Monte Carlo               | paths=100000                           | 4.620907 +/- 0.0295   |
# | Heston 1993               | v0=s2, k=2, th=s2, sv=0.3, rho=-0.5    | 4.577095              |
# | Bates 1996                | Heston + lam=1, mu_J=-0.05, sig_J=0.10 | 4.924756              |
# | P(ITM)                    | N(d2) bajo Q                           | 0.5299                |
# | P(Profit) vs BS price     | premio=4.6150                          | 0.3534                |
# | Greeks (delta/gamma/vega) | BS closed-form                         | d=+0.5695 g=+0.0393   |
# +---------------------------+----------------------------------------+-----------------------+

py scripts/option_pricing.py validate
# === Black-Scholes European ===
#   [OK] Hull 9th ed Example 15.6 (ATM call): got 4.7594, ref 4.7594
#   [OK] ... (5/5 pass)
# === American (Binomial N=2000) ===
#   [OK] Hull 9th ed Example 21.1: got 4.2841, ref 4.2841
#   [OK] ... (4/4 pass)
# === Put-Call Parity (BS) ===
#   [OK] C - P = 4.8770575499, S*exp(-qT) - K*exp(-rT) = 4.8770575499
# 0 failure(s)

from scripts.option_pricing import bs_price, binomial_price, mc_european_price, lsm_price, bs2_american_price, bs_greeks, implied_vol

# Pricing
c = bs_price(100, 100, 0.25, 0.05, 0.0, 0.20, "call")     # 4.615
p = binomial_price(100, 100, 0.25, 0.05, 0.0, 0.20, 500, "put", "european")

# Greeks (solo BS)
g = bs_greeks(100, 100, 0.25, 0.05, 0.0, 0.20, "call")
# -> {"delta": 0.569, "gamma": 0.039, "vega": 19.64, "theta": -10.47, "rho": 13.08}

# Implied vol
iv = implied_vol(4.62, 100, 100, 0.25, 0.05, 0.0, "call", "european")
# -> 0.2003