Large liquidity expansion of super-hedging costs
Abstract
We consider a financial market with liquidity cost as in Çetin, Jarrow and Protter [2004], 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 [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
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.