Semiparametric Upper Bounds for Option Prices

AndrewW. Lo

Rodney L. White Center for Financial Research Working Papers from Wharton School Rodney L. White Center for Financial Research

Abstract: In this paper, we derive upper bounds on call and put options which are priced via the risk-neutral valuation approach of Cox and Ross (1976) and Harrison and Kreps (1979). The upper bounds are shown to obtain across all terminal stock price distributions for which the associated equivalent martingale measures (EMM) have a common variance. Because the proposed upper bound depends only upon the variance of the EMM and not upon the entire distribution, the bound is termed "semiparametric" and must be satisfied for processes with jumps as well as diffusion components. The relation between the variance of the EMM and the empirically observable variance is derived and some illustrative empirical evidence is presented which suggests that these bounds may be of considerable practical value.

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