Leland's Strategy for a Constant Transaction Costs Rate

In 1985 Leland suggested an approach to price contingent claims under proportional transaction costs. Its main idea is to use the classical Black{Scholes formula with a suitably adjusted volatility for a periodical revision of the portfolio whose terminal value approximates the pay-o. Unfortunately, if the transaction costs rate does not depend on the number of revisions, the approximation error does not converge to zero as the frequency of revisions tends to innity. In the present paper, we suggest a modication of Leland's strategy ensuring that the