"""Option-related math helpers shared across strategies."""
from __future__ import annotations
import math
from typing import Optional
def norm_cdf(x: float) -> float:
return 0.5 * (1.0 + math.erf(x / math.sqrt(2.0)))
def black_scholes_price(
spot: float,
strike: float,
time_years: float,
rate: float,
sigma: float,
option_type: str,
) -> float:
if time_years <= 0 or sigma <= 0 or spot <= 0 or strike <= 0:
intrinsic = max(0.0, strike - spot if option_type == "P" else spot - strike)
return intrinsic
vol_term = sigma * math.sqrt(time_years)
d1 = (math.log(spot / strike) + (rate + 0.5 * sigma**2) * time_years) / vol_term
d2 = d1 - vol_term
if option_type.upper() == "P":
return strike * math.exp(-rate * time_years) * norm_cdf(-d2) - spot * norm_cdf(-d1)
return spot * norm_cdf(d1) - strike * math.exp(-rate * time_years) * norm_cdf(d2)
def estimate_implied_vol(
premium: float,
spot: float,
strike: float,
time_years: float,
option_type: str,
rate: float = 0.02,
iterations: int = 60,
) -> Optional[float]:
if premium <= 0 or time_years <= 0 or spot <= 0 or strike <= 0:
return None
low, high = 1e-4, 5.0
price_low = black_scholes_price(spot, strike, time_years, rate, low, option_type)
price_high = black_scholes_price(spot, strike, time_years, rate, high, option_type)
if premium < price_low or premium > price_high:
return None
for _ in range(iterations):
mid = 0.5 * (low + high)
price_mid = black_scholes_price(spot, strike, time_years, rate, mid, option_type)
if abs(price_mid - premium) < 1e-4:
return mid
if price_mid > premium:
high = mid
else:
low = mid
return 0.5 * (low + high)
