Hedging Option Portfolios in the Presence of Transaction Costs

Abstract

We derive a nonlinear parabolic partial differential equation for the value of portfolios of options in the presence of proportional transaction costs. This assumes a Leland world of transacting after each time interval, which is of fixed length. The equation reduces to the modified variance case described by Leland in the case of a single option. We demonstrate the nonlinear nature of option portfolios and give results for several simple combinations of options.