State prices implicit in valuation formulae for derivative securities:a martingale approach

Derivative assets analysis usually takes a model of the underlying price process as given and attempts to value derivative securities relative to that model. This paper studies the following "inverse" problem: given a valuation formula for a derivative asset, what can be inferred about the underlying asset price process? Assuming continuous sample paths, we show that a sufficiently regular pricing formula for some derivative asset completely determines the risk-neutral law of underlying price. In particular, such a valuation formula implies a unique set of state prices for payoffs contingent on the price path of the underlying security. As an illustration of our main result, we analyse certain pricing formulae for European options on zero-coupon bonds.