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Hedging of covered options with linear market impact and gamma constraint

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
Journal name
SIAM Journal on Control and Optimization
Volume
55
Number
5
Pages
3319–3348
Publication identifier
Metadata
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Author(s)
Bouchard, Bruno
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Loeper, Grégoire

Zou, Yiyi
Abstract (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.
Subjects / Keywords
Stochastic target; Hedging; Price impact