Large Liquidity Expansion of Super-Hedging Costs

Asymptotic Analysis, 79(1–2):45–64, 2012

Posted: 25 Jul 2022

See all articles by Dylan Possamaï

Dylan Possamaï

ETH Zürich

H. Mete Soner

Princeton University - Department of Operations Research & Financial Engineering (ORFE)

Nizar Touzi

Ecole Polytechnique, Paris

Date Written: March 6, 2012

Abstract

We consider a financial market with liquidity cost as in Çetin, Jarrow and Protter, where the supply function depends on a parameter ε, with ε=0 corresponding to the perfect liquid situation. Using the PDE characterization of Çetin, Soner and Touzi 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.

Keywords: super-replication, liquidity, viscosity solutions, asymptotic expansions

Suggested Citation

Possamaï, Dylan and Soner, H. Mete and Touzi, Nizar, Large Liquidity Expansion of Super-Hedging Costs (March 6, 2012). Asymptotic Analysis, 79(1–2):45–64, 2012, Available at SSRN: https://ssrn.com/abstract=4050935

Dylan Possamaï (Contact Author)

ETH Zürich ( email )

Raemistrasse 101
Raemistr. 101
Zurich, 8092
Switzerland

H. Mete Soner

Princeton University - Department of Operations Research & Financial Engineering (ORFE) ( email )

Sherrerd Hall, Charlton Street
Princeton, NJ 08544
United States

Nizar Touzi

Ecole Polytechnique, Paris ( email )

1 rue Descartes
Paris, 75005
France

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