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Arbitrage Values Generally Depend On A Parametric Rate of Return
Author(s) -
Brenner Robin J.,
Denny J. L.
Publication year - 1991
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.1991.tb00015.x
Subject(s) - martingale (probability theory) , mathematics , economics , arbitrage , mathematical economics , call option , infinitesimal , econometrics , short rate , interest rate , financial economics , finance , mathematical analysis , yield curve
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.