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I understand that the common way to arrive at an implied distribution for an underlying is through the price of its call options as per the Breeden-Litzenberger formula.

I am wondering if its possible to do it via looking at forwards or is it a lost cause since forwards are really just a function of the discount rate and dividend rate rather than an "implied" price?

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  • $\begingroup$ Might be better to add in a longer title $\endgroup$
    – KaiSqDist
    Feb 2 at 12:09

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You are right: the forward has no information about the future (market inferred) price distribution. In fact, under the risk-free measure, it is just the undiscounted expectation of the price, taking into account possible dividends, repo, borrowing costs, storage, etc (i.e. anything that could make the future contract more/less appealing than just buying the spot).

Therefore, to get some information about the density, you need some other financial contract that has some non-linearity and that depend on (and allow you to extract) this information. As you can see from Breeden-Litzenberger, the more options you have, the more resolution you can obtain for the distribution.

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