  We solve the superhedging problem for European options in an illiquid
extension of the Black-Scholes model, in which transactions have transient
price impact and the costs and the strategies for hedging are affected by
physical or cash settlement requirements at maturity. Our analysis is based on
a convenient choice of reduced effective coordinates of magnitudes at
liquidation for geometric dynamic programming. The price impact is transient
over time and multiplicative, ensuring non-negativity of underlying asset
prices while maintaining an arbitrage-free model. The basic (log-)linear
example is a Black-Scholes model with relative price impact being proportional
to the volume of shares traded, where the transience for impact on log-prices
is being modelled like in Obizhaeva-Wang \cite{ObizhaevaWang13} for nominal
prices. More generally, we allow for non-linear price impact and resilience
functions. The viscosity solutions describing the minimal superhedging price
are governed by the transient character of the price impact and by the physical
or cash settlement specifications. Pricing equations under illiquidity extend
no-arbitrage pricing a la Black-Scholes for complete markets in a
non-paradoxical way (cf.\ {\c{C}}etin, Soner and Touzi
\cite{CetinSonerTouzi10}) even without additional frictions, and can recover it
in base cases.

Pricing of Securities;Probability;Trading and Market Microstructure