Abstract
Let X denote a positive Markov stochastic integral, and let S(t, μ) = exp(μt)X(t) represent the price of a security at time t with infinitesimal rate of return μ. Contingent claim (option) pricing formulas typically do not depend on μ. We show that if a contingent claim is not equivalent to a call option having exercise price equal to zero, then security prices having this property—option prices do not depend on μ—must satisfy: for some V (0, T), In(S(t, μ)X(V)) is Gaussian on a time interval [V, T], and hence S(t, μ) has independent observed returns. With more assumptions, V= 0, and there exist equivalent martingale measures.
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