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We know of plenty ways to extract risk neutral distirbutions from option prices (for example Breeden Litzberger) but there is no real analysis on how to interpret negative state prices (Haug 2007 for example). State prices are Arrow Debreu securities, so it is the price an agent is willing to pay to get $1\$$ in a particular state and $0$ else.

Doing equilibirum and utility maximization we know that the agents smoothen their consumption by marginal rate of substitution which describes their risk-aversion.

Coming back to the negative probabilties: Could it not be possible there exist actual economic states where the agent is receiving money for the contract?

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Negative state prices in equilibrium can only occur if the utility of wealth is not always strictly positive. A natural assumption on utility is that it is strictly increasing in wealth in all states of nature (more money is always preferred to less money). Thus, unless you can come up with a situation in which an agent would prefer to be less wealthy and everything else equal there should not be negative state prices.

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  • $\begingroup$ I would add that I interpret Haug (2007) to be intended in a humorous or whimsical, not serious vein. $\endgroup$
    – nbbo2
    Nov 23, 2015 at 14:16

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