What's the difference between Black's model and Black–Scholes Model? Aren't they same and can be used to price European options?

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The Black model is used to price options on futures. It’s slightly different from the BSM model: note that the (continuously-compounded) risk-free rate doesn’t appear in the formula for d1.

Thank you…

Can we say that Black Scholes is not only for equity stock options but black’s model is for options in future, bond and also covers stocks as well.

Black-Scholes-Merton is for options on stocks, and I suspect that it works well for options on commodities as well. But not for options on bonds (because their price depends directly on interest rates).

Black’s model is for options on stock futures, and I suspect that it works well for commodity futures as well. But probably not for bond futures (for the same reason).

Great Thank You!

My pleasure.

  1. Is the absence of r the only difference in black model from black scholes?

  2. if used for options on interest rate futures, would there be much difference in prices through both?

  3. which method is used in pricing most of the exchange traded options on interest rate futures?

  1. Not sure.

  2. We can’t use BSM for options on interest rate futures because it assumes a constant risk-free rate.

  3. I believe the text says that the Black model can be used equity index futures, caps, floors, and swaptions. Caps and floors are series of interest rate options.


Can black model be used for european bond options with futures or spot, either as underlying ? I kinda read it in Hull J. C.