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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 publié
Date
2012
Journal name
Asymptotic Analysis
Volume
79
Number
1-2
Publisher
IOS Press
Pages
45-64
Publication identifier
Metadata
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Author(s)
Possamaï, Dylan
CEntre 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 expansions
JEL
G1 - General Financial Markets