Greeks Intuition

The Greeks measure how sensitive an option's price is to each of its inputs — literally the PARTIAL DERIVATIVES of the Black-Scholes formula, from the Calculus Review course, applied to option pricing. Delta (sensitivity to the stock price) is the most important one:

import math
from statistics import NormalDist

def bs_call_price(S, K, T, r, sigma):
    d1 = (math.log(S / K) + (r + sigma**2 / 2) * T) / (sigma * math.sqrt(T))
    d2 = d1 - sigma * math.sqrt(T)
    N = NormalDist().cdf
    return S * N(d1) - K * math.exp(-r * T) * N(d2)

def delta_numerical(S, K, T, r, sigma, h=0.01):
    return (bs_call_price(S + h, K, T, r, sigma) - bs_call_price(S - h, K, T, r, sigma)) / (2 * h)

This is the EXACT central-difference technique from the Calculus Review course's numerical_derivative — Delta really is just "the derivative of option price with respect to stock price," nothing more exotic than that.

Vega measures sensitivity to volatility — nudge sigma instead of S, same central-difference technique:

def vega_numerical(S, K, T, r, sigma, h=0.0001):
    return (bs_call_price(S, K, T, r, sigma + h) - bs_call_price(S, K, T, r, sigma - h)) / (2 * h)

Notice h is much smaller here (0.0001 vs. 0.01) — sigma itself is usually a small number (0.1-0.5 is a typical range), so a proportionally smaller nudge keeps the finite-difference approximation accurate. Every other Greek (Gamma — sensitivity of Delta itself; Theta — sensitivity to time; Rho — sensitivity to interest rate) follows the exact same pattern: pick the input, nudge it by a small h, take the central difference.