The Black model (sometimes known as the Black-76 model) is a variant of the Black-Scholes option pricing model.
Its primary applications are for pricing bond options, interest rate caps / floors, and swaptions.
It was first presented in a paper written by Fischer Black in 1976.


To calculate an option on a futures contract we use the Black-Scholes with 2 modifications.
The underlier is a futures contract potentially initiated at time t (expiration) and going on to a delivery date we will call t' (t prime)
Therefore the futures contract we might do at experation is F(t,t')


Notice that we have 3 dates.
a) the date the option is executed (t0)
b) the date the option expires and the future commerces (t)
c) the date the futures contract delivers (t')


Modification 1

Replace the S factor with F(to, t')


Modification 2

To account for daily interest received on a replicating portfolio including lent funds in the amount of F(t0, t') we treat the underlier as if it has a continuous dividend, using risk-free interest rate for the "dividend" rate










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