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 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 [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.
Original language | English (US) |
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Pages (from-to) | 45-64 |
Number of pages | 20 |
Journal | Asymptotic Analysis |
Volume | 79 |
Issue number | 1-2 |
DOIs | |
State | Published - 2012 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- General Mathematics
Keywords
- asymptotic expansions
- liquidity
- super-replication
- viscosity solutions