# Option Greeks' Formulas for Black & Scholes vs Black 76

I know Black76 uses forward prices instead of spot and that D1 calculation doesn't use the interest rate. Are there any other differences between the two?

I'm calculating: theoretical value, delta, lambda, vega, theta, rho, gamma

• In the BS formulas, replace every occurrence of $S$ with $F e^{-rT}$ and you have the corresponding Black76 formulas. They are the result of a mechanical substitution of symbols, followed by simplification if appropriate (so it is not that "d1 does not use interest rate", rather "+r and -r cancel out in the expression for d1"). – Alex C May 18 '18 at 15:04

## 1 Answer

There is no fundamental/assumptional difference between these two models. The only difference is Black 76 reflects interest rate, cost of carries, dividend etc. on the forward price, while Black Scholes treats them as separate components of the model.

In the formulas of calculating D1, the only difference in addition to the change of S - >F is that Black76 doesn't have "r" component in the nominator because r has already been priced in F.