03-greeks.md

Greeks

Greeks are option-price sensitivities. They make a portfolio's exposure legible without repricing every scenario from scratch.

Greek	Definition	Meaning
Delta $\Delta$	$\partial P / \partial F$	Hedge ratio versus the forward.
Gamma $\Gamma$	$\partial^2 P / \partial F^2$	How quickly delta changes.
Vega $\nu$	$\partial P / \partial \sigma$	Price change per 1.00 vol shift.
Theta $\Theta$	$\partial P / \partial T$	Value of more time to expiry.
Rho $\rho$	$\partial P / \partial r$	Rate sensitivity; zero in this app's convention.

Black-76 Forms

$$ \begin{aligned} \Delta_{call} &= df \cdot \Phi(d_1) \\ \Delta_{put} &= df \cdot (\Phi(d_1)-1) \\ \Gamma &= \frac{df \cdot \varphi(d_1)}{F\sigma\sqrt{T}} \\ \nu &= df \cdot F \cdot \varphi(d_1) \cdot \sqrt{T} \\ \Theta &= \frac{df \cdot F \cdot \varphi(d_1) \cdot \sigma}{2\sqrt{T}} \end{aligned} $$

Vega and gamma are the same for calls and puts. Delta carries the call/put direction.

Units

The implementation returns forward-denominated Greeks. Deribit publishes coin-denominated Greeks, so compare units before comparing numbers:

• Coin delta is approximately forward delta divided by $F$.
• Coin vega is approximately forward vega divided by $F$.
• Theta sign conventions differ by venue; this app reports $\partial P / \partial T$.

Finite-difference tests check delta, gamma, and vega against the pricer.