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

Lépinette, Emmanuel; Darses, Sébastien

Lépinette, Emmanuel; Darses, Sébastien (2014), Mean Square Error and Limit Theorem for the Modi fied Leland Hedging Strategy with a Constant Transaction Costs Coefficient, in Zariphopoulou, Thaleia; Rutkowski, Marek; Kabanov, Yuri, Inspired by Finance. The Musiela Festschrift, Springer : Berlin, p. 159-199

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Type

Chapitre d'ouvrage

Date

2014

Book title

Inspired by Finance. The Musiela Festschrift

Book author

Zariphopoulou, Thaleia; Rutkowski, Marek; Kabanov, Yuri

Publisher

Springer

Published in

Berlin

ISBN

978-3-319-02068-6

Pages

159-199

Abstract (EN)

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.

Subjects / Keywords

martingale limit theorem; asymptotic hedging; Leland-Lott strategy; transaction costs

JEL

D23 - Organizational Behavior; Transaction Costs; Property Rights