Black model is an option pricing model used in calculation of value and Greeks of vanilla call and put options where underlying is a forward contract \(F\).
The payoff of the option at the exercise time \( T \) is (with strike = \(K\)):

Call:

\( \max\left(F-K,0\right) \)

Put:

\( \max\left(K-F,0\right) \)

Straddle (Call + Put):

\( \max\left(F-K,0\right) + \max\left(K-F,0\right) \)