Hedging of covered options with linear market impact and gamma constraint

Bruno Bouchard (), G Loeper and Y Zou
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Bruno Bouchard: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique
G Loeper: Monash University [Clayton], FiQuant - Chaire de finance quantitative - MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec
Y Zou: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique

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Abstract: Within a financial model with linear price impact, we study the problem of hedging a covered European option under gamma constraint. Using stochastic target and partial differential equation smoothing techniques, we prove that the super-replication price is the viscosity solution of a fully non-linear parabolic equation. As a by-product, we show how ε-optimal strategies can be constructed. Finally, a numerical resolution scheme is proposed.

Keywords: Price impact; Hedging; Stochastic target (search for similar items in EconPapers)
Date: 2017
Note: View the original document on HAL open archive server: https://hal.science/hal-01247523v1
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Citations: View citations in EconPapers (14)

Published in SIAM Journal on Control and Optimization, 2017, 55 (5), pp.3319-3348. ⟨10.1137/15m1054109⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01247523

DOI: 10.1137/15m1054109

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