Optimal discretization of hedging strategies with directional views

Abstract : We consider the hedging error of a derivative due to discrete trading in the presence of a drift in the dynamics of the underlying asset. We suppose that the trader wishes to find rebalancing times for the hedging portfolio which enable him to keep the discretization error small while taking advantage of market trends. Assuming that the portfolio is readjusted at high frequency, we introduce an asymptotic framework in order to derive optimal discretization strategies. More precisely, we formulate the optimization problem in terms of an asymptotic expectation-error criterion. In this setting, the optimal rebalancing times are given by the hitting times of two barriers whose values can be obtained by solving a linear-quadratic optimal control problem. In specific contexts such as in the Black-Scholes model, explicit expressions for the optimal rebalancing times can be derived.
Type de document :
Pré-publication, Document de travail
2014
Liste complète des métadonnées


https://hal.archives-ouvertes.fr/hal-01024975
Contributeur : Jiatu Cai <>
Soumis le : mercredi 16 juillet 2014 - 22:39:49
Dernière modification le : mardi 11 octobre 2016 - 15:20:21
Document(s) archivé(s) le : lundi 24 novembre 2014 - 17:10:50

Fichiers

Discrete_Delta_Hedge_submitted...
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01024975, version 1
  • ARXIV : 1407.4570

Collections

INSMI | UPMC | PMA | USPC

Citation

Jiatu Cai, Masaaki Fukasawa, Mathieu Rosenbaum, Peter Tankov. Optimal discretization of hedging strategies with directional views. 2014. <hal-01024975>

Partager

Métriques

Consultations de
la notice

292

Téléchargements du document

85