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I have some questions regarding pricing futures options and I just want to be sure that my thoughts are correct.

I am trying to price options on futures for american & european style.

In the latest case, I am using the Black Model.

When looking at the volatility of the contract Ito's lemma gives that the volatility of the future contract is the same as the volatility of the underlying (in the future contract). Is it correct?

Then if I want to use Black Model, I just need to compute the volatility of the futures' underlying.

Options on future are generally american. Then I am using a binomial tree to price my future contracts. Here again the volatility is then determined by the future underlying.

Is that correct?

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it depends on asset class. In some classes, the future is more liquid than the underlying eg oil so it makes more sense to work with its volatility.

Also, the forward price and the spot price only have the same volatility if we assume deterministic interest rates. For short-dated equity type products, this is reasonable. For long-dated products and interest rate products, this is not a good modelling assumption.

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When looking at the volatility of the contract Ito's lemma gives that the volatility of the future contract is the same as the volatility of the underlying (in the future contract). Is it correct?

CORRECT

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  • $\begingroup$ Yes it is correct :) $\endgroup$
    – ALFRAM
    Commented Mar 8, 2017 at 18:13

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