For a cross-section of strike prices, market index (or ETF) option values reveal the distribution of wealth under the risk-neutral measure. The cost to an investor of making small changes to the strike price of a given option equals the physical probability of being at the money multiplied by the marginal value of a dollar when that happens. This only works for a representative market index or ETF, because options on any other underlyer will incorporate payoff probabilities specific to the underlyer. In the case of the market underlyer, we say the options reveal the distribution of state prices .
The connection between options and state prices is valuable for several reasons, not least of which is the identification of true probabilities, which is possible under certain circumstances. Whether or not the physical probabilities can be identified, there are handful of important implications for investing in options markets.
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