Mean Square Error and Limit Theorem for the Modified Leland Hedging Strategy with a Constant Transaction Costs Coefficient

Abstract

We study the Leland model for hedging portfolios in the presence of a constant proportional transaction costs coefficient. The modified Leland's strategy defined in [2], contrarily to the classical one, ensures the asymptotic replication of a large class of payoff. In this setting, we prove a limit theorem for the deviation between the real portfolio and the payoff. As Pergamenshchikov did in the framework of the usual Leland's strategy [11], we identify the rate of convergence and the associated limit distribution. This rate turns out to be improved using the modified strategy and non periodic revision dates.

Keywords: asymptotic hedging, Leland-Lott strategy ,transaction costs, martingale limit theorem