Hedging of covered options with linear market impact and gamma constraint

Bouchard, Bruno; Loeper, Grégoire; Zou, Yiyi

Bouchard, Bruno; Loeper, Grégoire; Zou, Yiyi (2017), Hedging of covered options with linear market impact and gamma constraint, SIAM Journal on Control and Optimization, 55, 5, p. 3319–3348. 10.1137/15M1054109

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Type

Article accepté pour publication ou publié

Date

2017

Nom de la revue

SIAM Journal on Control and Optimization

Volume

Numéro

Pages

3319–3348

Identifiant publication

10.1137/15M1054109

Métadonnées

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Auteur(s)

Bouchard, Bruno
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Loeper, Grégoire

Zou, Yiyi

Résumé (EN)

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.