MINIMIZING TRANSACTION COSTS OF OPTION HEDGING STRATEGIES

E. R. Grannan and G. H. Swindle

Mathematical Finance, 1996, vol. 6, issue 4, 341-364

Abstract: This paper introduces a method for constructing option hedging strategies in the presence of transaction costs. the approach begins with the prescription of a large, but tractable class of strategies. A variational problem is constructed in which the expected square replication error is minimized subject to a fixed initial portfolio value from among the class of strategies. the solution of this variational problem results in a replicating strategy which simulations show outperforms strategies previously considered. We illustrate this method in a particular class of strategies which contains Leland's discrete time replication scheme. We show that a strategy which uses varying time intervals between hedging can significantly reduce replication error for a given initial wealth. We will also construct and assess strategies obtained by optimizing a mean‐variance criterion. This methodology extends to other optimization problems involving initial portfolio value and expected square replication error, as well as to other classes of strategies.

Date: 1996
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