%0 Journal Article
%T Large liquidity expansion of super-hedging costs
%A Dylan Possama£¿
%A Nizar Touzi
%A H. Mete Soner
%J Quantitative Finance
%D 2012
%I arXiv
%R 10.3233/ASY-2011-1089
%X We consider a financial market with liquidity cost as in \c{C}etin, Jarrow and Protter [2004], where the supply function $S^{\epsilon}(s,\nu)$ depends on a parameter $\epsilon\geq 0$ with $S^0(s,\nu)=s$ corresponding to the perfect liquid situation. Using the PDE characterization of \c{C}etin, Soner and Touzi [2010] 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 $\epsilon$. 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.
%U http://arxiv.org/abs/1208.3785v2