0DTE Index Options Microstructure: Dealer Gamma Exposure (GEX), Vanna, and Charm Flows in Python

Canonical Research Note: Originally published by the TrendSpike Institutional Systems & Quantitative Finance Desk. Full Black-Scholes-Merton second-order Greek derivations and dealer hedging matrices are available in the primary publication.

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Python Implementation: Black-Scholes 0DTE Gamma, Vanna & Charm Engine

python
import math

def norm_pdf(x: float) -> float:
    return math.exp(-0.5 * x * x) / math.sqrt(2.0 * math.pi)

def compute_0dte_greeks(spot: float, strike: float, iv: float, minutes_left: float, rate: float = 0.05) -> dict:
    tau = max(minutes_left / (252.0 * 390.0), 1e-6)
    sqrt_tau = math.sqrt(tau)
    d1 = (math.log(spot / strike) + (rate + 0.5 * iv * iv) * tau) / (iv * sqrt_tau)
    d2 = d1 - iv * sqrt_tau
    pdf_d1 = norm_pdf(d1)

    gamma = pdf_d1 / (spot * iv * sqrt_tau)
    vanna = -pdf_d1 * (d2 / iv)
    charm = pdf_d1 * ((2.0 * rate * tau - d2 * iv * sqrt_tau) / (2.0 * tau * iv * sqrt_tau))

    return {
        "gamma": round(gamma, 6),
        "vanna": round(vanna, 6),
        "charm_daily": round(charm / 252.0, 6),
    }