Black_Scholes_option_pricing.py

import scipy.stats as st
import numpy as np


def black_scholes_pricing_model(
    option_type: str, 
    s: float, 
    k: float, 
    r: float, 
    v: float, 
    q: float, 
    t: float
) -> float:
    """
    Parameters:
        option_type: option type, use 'call' or 'put'
        s: spot price
        k: strike price
        r: interest rate
        v: volatility
        q: yield rate
        t: maturity(year)
    """

    d1 = (np.log(s / k) + (r - q + v**2 / 2) * t) / (v * t**0.5)
    d2 = d1 - v * t**0.5

    call = s * st.norm.cdf(d1) - k * np.exp(-r * t) * st.norm.cdf(d2)
    put = k * np.exp(-r * t) * st.norm.cdf(-d2) - s * st.norm.cdf(-d1)

    if option_type == "call":
        return max(call, 0)
    elif option_type == "put":
        return max(put, 0)
    else:
        raise ValueError("Wrong option input.")