Robert H. Litzenberger studied state-contingent claim prices with Douglas T. Breeden. Their call-spread argument relates derivatives of call option prices with respect to strike to state prices. Under suitable smoothness, the second derivative yields a discounted density, providing a bridge between observable option pricing and the pricing of narrow ranges of future asset values.[ref]
Prices of State-Contingent Claims Implicit in Option Prices by Douglas T. Breeden and Robert H. Litzenberger. Section II, pages 625–627 and equation (2)
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