Arbitrage Values Generally Depend On A Parametric Rate of Return

Let "X" denote a positive Markov stochastic integral, and let "S"("t", μ) = exp(μ"t")"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. Copyright 1991 Blackwell Publishers.