Large liquidity expansion of super-hedging costs

Dylan Possamaï, H. Mete Soner, Nizar Touzi

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

We consider a financial market with liquidity cost as in [Çetin, Jarrow and Protter, Finance and Stochastics 8 (2004), 311-341], where the supply function S ε(s,ν) depends on a parameter ε≥0 with S 0(s,ν)=s corresponding to the perfect liquid situation. Using the PDE characterization of Çetin, Soner and Touzi [Finance and Stochastics 14(3) (2010), 317-341], 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 ε. 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.

Original languageEnglish (US)
Pages (from-to)45-64
Number of pages20
JournalAsymptotic Analysis
Volume79
Issue number1-2
DOIs
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • asymptotic expansions
  • liquidity
  • super-replication
  • viscosity solutions

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