We consider a financial market with liquidity cost as in Cetin, Jarrow and Protter [2004], where the supply function S \epsilon (s, \nu ) depends on a parameter \epsilon%DIFDELCMD < }\geq0 %%% with S0 (s, \nu )=s corresponding to the perfect liquid situation. Using the PDE characterization of Cetin, 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.
We consider a financial market with liquidity cost as in Cetin, Jarrow and Protter [2004], where the supply function S ^{\epsilon (s, \nu ) depends on a parameter %DIFDELCMD < }\geq0 %%% \epsilon\geq 0 with S^0 (s, \nu )=s corresponding to the perfect liquid situation. Using the PDE characterization of Cetin, 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.
R
\epsilon
^{\epsilon
R
\nu
\nu
D
\epsilon
R
with S0
\epsilon\geq 0 with S^0
R
\nu
\nu
D
,
R
\epsilon
\epsilon