black_scholes.py

from scipy.stats import norm
import numpy as np


N = norm.cdf


def d1_d2(S: float, K: float, T: float, r: float, sigma: float):
    d1 = (np.log(S / K) + (r + sigma ** 2 / 2) * T) / (sigma * np.sqrt(T))
    d2 = d1 - sigma * np.sqrt(T)
    return d1, d2


def BS_CALL(S: float, K: float, T: float, r: float, sigma: float) -> float:
    """Black-Scholes model for a CALL option

    Args:
        S (float): Current price
        K (float): Strike price
        T (float): Time (% p.a.)
        r (float): Risk-free rate (% p.a.)
        sigma (float): Volatility

    Returns:
        float: price
    """
    d1, d2 = d1_d2(S, K, T, r, sigma)
    return S * N(d1) - K * np.exp(-r * T) * N(d2)


def BS_PUT(S, K, T, r, sigma) -> float:
    """Black-Scholes model for a PUT option

    Args:
        S (float): Current price
        K (float): Strike price
        T (float): Time (% p.a.)
        r (float): Risk-free rate (% p.a.)
        sigma (float): Volatility

    Returns:
        float: price
    """
    d1, d2 = d1_d2(S, K, T, r, sigma)
    return K * np.exp(-r * T) * N(-d2) - S * N(-d1)