Hedging Under an Expected Loss Constraint with Small Transaction Costs

42 Pages Posted: 21 Oct 2014 Last revised: 9 Dec 2016

See all articles by Bruno Bouchard

Bruno Bouchard

Université Paris Dauphine - CEREMADE

Ludovic Moreau

ETH Zürich - Department of Mathematics

Halil Mete Soner

ETH Zürich; Swiss Finance Institute

Date Written: March 8, 2016

Abstract

We consider the problem of option hedging in a market with proportional transaction costs. Since super-replication is very costly in such markets, we replace perfect hedging with an expected loss constraint. Asymptotic analysis for small transaction costs is used to obtain a tractable model. A general expansion theory is developed using the dynamic programming approach. Explicit formulae are obtained in the special cases of exponential and power utility functions. As a corollary, we retrieve the asymptotics for the exponential utility indifference price.

Keywords: Expected loss constraint, hedging, transaction cost, asymptotic expansion

JEL Classification: C61; G11

Suggested Citation

Bouchard, Bruno and Moreau, Ludovic and Soner, Halil Mete, Hedging Under an Expected Loss Constraint with Small Transaction Costs (March 8, 2016). Swiss Finance Institute Research Paper No. 14-60, Available at SSRN: https://ssrn.com/abstract=2512205 or http://dx.doi.org/10.2139/ssrn.2512205

Bruno Bouchard

Université Paris Dauphine - CEREMADE ( email )

Place du Marechal de Lattre de Tassigny
Paris Cedex 16, 75775
France

Ludovic Moreau

ETH Zürich - Department of Mathematics ( email )

R¨amistrasse 101
Raemistr. 101
Z¨urich, 8092
Switzerland

Halil Mete Soner (Contact Author)

ETH Zürich ( email )

Zürichbergstrasse 18
8092 Zurich, CH-1015
Switzerland

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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