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## STATE-PRICE DENSITY APPROACH FROM CALL PRICES

Breeden-Litenberger 1978 (BreedenLitzenberger78) and Dupire (1994) (dupire-PricingSmile) are making a nontrivial claim about

$\frac{\partial^2 C}{\partial K^2}$

They are telling us that from this second derivative we are obtaining an interesting object: the state-price density of theoretical Arrow-Debreu securities that pay \$1 in $T$ periods if the asset has value $M$ and nothing otherwise.

Interesting questions may be that given that the risk-neutral valuation assumption is that all assets should give us the risk-free rates whether we can get information tying these things across many stocks and what the best way to deal with missing data is for the volatility surface.  This is a practical problem for me at the moment while testing stochastic volatility models.