By Dylan Possamai, H. Mete Soner & Nizar Touzi (Cahier de la Chaire n°35)
We consider a financial market with liquidity cost as in Cetin, Jarrow and Protter (2004) where the supply function depends on a parameter with corresponding to the perfect liquid situation. Using the PDE characterization of Cetin, Soner and Touzi (2007) 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.
Key words: Super-replication, liquidity, viscosity solutions, asymptotic expansions