
Large liquidity expansion of super-hedging costs
Possamaï, Dylan; Soner, Halil Mete; Touzi, Nizar (2012), Large liquidity expansion of super-hedging costs, Asymptotic Analysis, 79, 1-2, p. 45-64. http://dx.doi.org/10.3233/ASY-2011-1089
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Type
Article accepté pour publication ou publiéDate
2012Journal name
Asymptotic AnalysisVolume
79Number
1-2Publisher
IOS Press
Pages
45-64
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Possamaï, DylanCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Soner, Halil Mete
Touzi, Nizar
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We consider a financial market with liquidity cost as in Cetin, Jarrow and Protter [3] where the supply function S"(s; ) depends on a parameter " 0 with S0(s; ) = s corresponding to the perfect liquid situation. Using the PDE characterization of Cetin, Soner and Touzi [6] of the super-hedging cost of an option written on such a stock, we provide a Taylor expansion of the super-hedging cost in powers of ". In particular, we explicitly compute the first term in the expansion for a European Call option and give bounds for the order of the expansion for a European Digital Option.Subjects / Keywords
Super-replication; liquidity; viscosity solutions; asymptotic expansionsRelated items
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