"""Vega: reference implementation.

Source: https://quantcore-labs.com/glossary/vega/
License: MIT (c) 2026 QuantCore Labs
Requires: Python 3.9+, scipy
"""
from math import exp, log, sqrt
from scipy.stats import norm

def bs_vega(S, K, T, r, sigma, q=0.0) -> float:
    """Black-Scholes-Merton vega per 1 volatility point (dPrice / dσ / 100).

    Same value for a European call and put. S, K, T, sigma must be positive.
    """
    if S <= 0 or K <= 0 or T <= 0 or sigma <= 0:
        raise ValueError("S, K, T and sigma must be positive")
    d1 = (log(S / K) + (r - q + 0.5 * sigma * sigma) * T) / (sigma * sqrt(T))
    return float(S * exp(-q * T) * norm.pdf(d1) * sqrt(T) / 100.0)