Semi-parametric upper bounds for option prices and expected payoffs

Abstract

Upper bounds on the expected payoff of call and put options are derived. These bounds depend only on the mean and variance of the terminal stock price and not on its entire distribution, so they are termed semi-parametric. A corollary of this result is a set of upper bounds for option prices obtained by the risk-neutral valuation approach of Cox and Ross. As an example, these bounds are shown to obtain across both lognormal diffusions and mixed diffusion-jump processes for any given data set. We present an illustrative example that suggests these bounds may be of considerable practical value.

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