Modified Leland’s Strategy for a Constant Transaction Costs Rate
Mathematical Finance, Forthcoming
12 Pages Posted: 13 Apr 2012
Date Written: February 12, 2012
Abstract
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-off. 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 infinity. In the present paper, we suggest a modification of Leland’s strategy ensuring that the approximation error vanishes in the limit.
Keywords: Black–Scholes formula, transaction costs, Leland’s strategy, approximate hedging
JEL Classification: G11
Suggested Citation: Suggested Citation