Module black76 

Black-76 (1976): European options on a future/forward price F.

Two settlement styles:

• Discounted (standard Black-76): the premium is paid up front and the payoff is discounted, call = e^{-rT}[F N(d1) - K N(d2)].
• Margined (futures-style / “future-style”): the option premium is itself margined daily like the future, so there is no discounting, call = F N(d1) - K N(d2). Common for options on futures on many non-US derivatives exchanges (e.g. Eurex, ICE, ASX).

F is the futures price directly — Black-76 has no spot, dividend or carry, since a future already embeds the cost of carry. All Greeks are sensitivities with respect to F (delta/gamma), sigma, r and time.

Enums

FuturesSettlement

How an option on a future is settled.

Functions

delta

Delta with respect to the futures price F.

gamma

Gamma with respect to the futures price F (same for calls and puts).

price

Black-76 price of a European option on a future.

rho

Rho (sensitivity to the risk-free rate). Zero for margined options, which have no discounting; -T * price for discounted options (the futures price is exogenous, so r enters only through the discount).

theta

Theta (calendar time decay, dV/dt = -dV/dT).

vega

Vega (per unit of vol; same for calls and puts).