# Measure for probabilities inferred from prices of derivatives on non-traded random variables?

Are probabilities of certain events (e.g. amount of rainfall over a period, probability of a Fed rate hike) inferred from derivatives on non-tradeable random variables (e.g. Weather Futures, Fed Funds Futures) stated in the risk-neutral measure (with the money market numeraire) or real-world measure?

Risk-neutral measures’ existence is a consequence of the FTAP, based on possible replication strategies for contingent claims. Either you can risklessly replicate the payments for such an asset, and the risk-neutral measure used to price it is unique because the no-arbitrage price, which is the value of the replicating portfolio, is unique. If you cannot replicate the claim, there is a range of NA prices (e.g. for a call option, it is $$\left[ \left[PV\left(F_T - K\right)\right]^+, PV(F_T) \right]$$, $$F_T$$ being the underlying’s forward price and $$PV$$ the present value) and infinitely many risk-neutral measures. For no reason should any one of them be particularly informative about real-world probabilities.