Product Title

import numpy as np
from scipy.stats import norm

def calculate_greeks(S: float, K: float, T: float, r: float, sigma: float, q: float = 0.0):
    """Vectorized production Greeks computation for trading desks."""
    d1 = (np.log(S / K) + (r - q + 0.5 * sigma ** 2) * T) / (sigma * np.sqrt(T))
    d2 = d1 - sigma * np.sqrt(T)
    delta = np.exp(-q * T) * norm.cdf(d1)
    gamma = (np.exp(-q * T) * norm.pdf(d1)) / (S * sigma * np.sqrt(T))
    vega = S * np.exp(-q * T) * np.sqrt(T) * norm.pdf(d1)
    return {"delta": float(delta), "gamma": float(gamma), "vega": float(vega)}