Affiliations: CMAP, Ecole Polytechnique, Paris, France. E-mails: {dylan.possamai, nizar.touzi}@polytechnique.edu | ETH (Swiss Federal Institute of Technology), Zurich, Switzerland. E-mail: hmsoner@ethz.ch
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 Sε(s,ν) depends on a parameter ε≥0 with S0(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.
