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Large liquidity expansion of super-hedging costs

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Date
2012
Dewey
Probabilités et mathématiques appliquées
Sujet
Super-replication; liquidity; viscosity solutions; asymptotic expansions
JEL code
G1
Journal issue
Asymptotic Analysis
Volume
79
Number
1-2
Publication date
2012
Article pages
45-64
Publisher
IOS Press
DOI
http://dx.doi.org/10.3233/ASY-2011-1089
URI
https://basepub.dauphine.fr/handle/123456789/5526
Collections
  • Chaire Finance et développement durable - Approches quantitatives
Metadata
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Author
Possamaï, Dylan
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Soner, Halil Mete
Touzi, Nizar
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Article accepté pour publication ou publié
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.

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