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So I got risk neutral probabilities from stock option prices. How can I then map them to a physical measure?

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You don't need to map them to the physical measure. Please read any of the basic option valuation text books or papers and it should become clearer. –  Matt Wolf Oct 10 '13 at 8:53
    
@MattWolf, need is very subjective. –  Ryogi Oct 13 '13 at 1:12
    
@Ryogi, care to comment on what you mean with that? If we could always recover the asset price distributions under the general risk measure then why would we use translation tools such as Black Scholes in the first place? If we know the exact price and return distributional properties and therefore know the payoff probabilities of contingent claims then we do not have to bother with risk neutral probabilities. Obviously that is not the case hence my point that we do not "need" the physical measure (other than of course for educational entertainment) –  Matt Wolf Oct 13 '13 at 1:54
    
Sorry, let me be a little more precise. We would still need risk neutral probability measures even if we know the exact distributional properties of the underlying asset because we still do not know the real expected return as a result of unknown utility. But what I see as the biggest problem is that the real distributional properties are unstable, they are dynamic and exhibit very little cointegration, so what is the point of wanting to "recover" them? –  Matt Wolf Oct 13 '13 at 1:58
    
To get an estimate of the market's forecast of returns. –  Ryogi Oct 13 '13 at 4:10

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You can use the Recovery Theorem.

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