Why Forward Prices Do Not Reveal the Implied Price Distribution

Summary

The note asks whether an underlying’s risk-neutral implied distribution can be recovered from forward prices, as it can from a cross-section of option prices using the Breeden–Litzenberger relationship. The answer explains that a forward price alone does not provide the distribution’s shape; it primarily reflects the discounted expectation under the risk-neutral measure, adjusted for carrying costs and benefits such as dividends, financing, borrowing, or storage.

To infer distributional detail, the market data must include contracts whose payoffs respond nonlinearly to the underlying price. Options across different strikes provide that information, with denser strike coverage allowing a more finely resolved estimate. The explanation is conceptual and does not derive the formula or discuss practical estimation issues such as sparse strikes, quote quality, or model assumptions.

Key ideas

• A forward price alone does not identify the underlying’s full risk-neutral price distribution.
• Forwards reflect an expectation adjusted for dividends and other carry costs or benefits.
• Distribution shape requires information from contracts with nonlinear payoffs.
• Option prices across strikes can reveal distributional detail, with greater strike coverage improving resolution.

Tags

# Implied Distributions from forward prices


# Implied Distributions from forward prices












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?

## Answer by KT8 (score 3)

https://quant.stackexchange.com/a/78185

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.