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.
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Pré-publication, Document de travail
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Contributeur : Jiatu Cai <>
Soumis le : mercredi 16 juillet 2014 - 22:39:49
Dernière modification le : vendredi 4 janvier 2019 - 17:32:34
Document(s) archivé(s) le : lundi 24 novembre 2014 - 17:10:50


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


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



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