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

Emmanuel Denis (1) , Sebastien Darses (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

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.

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

Domaines: Probabilités [math.PR]

Emmanuel Denis, Sebastien Darses. Mean Square Error and Limit Theorem for the Modi fied Leland Hedging Strategy with a Constant Transaction Costs Coefficient. The Musiela Festschrift, 2012, Forthcoming. (Forthcoming), pp.Forthcoming. ⟨hal-00700849⟩