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Graduate School of Management, University of California at Irvine; Oakley Sutton Management Corporation; and University of California at Irvine and Oakley Sutton Management Corporation, respectively. An earlier version of the paper was presented at the TIMS/CORSA Conference, Toronto, Ontario, Canada in May 1981. We thank Charles Zarzecki for a detailed description of order execution and for comments on an earlier version of the paper. Readers unfamiliar with options are referred to a forthcoming book by John Cox and Mark Rubinstein  which provides an up-to-date and insightful presentation of the topi.