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arXiv · 1208.3785

Large liquidity expansion of super-hedging costs

Dylan Possamaï·Nizar Touzi·H. Mete Soner
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Abstract

We consider a financial market with liquidity cost as in \c{C}etin, Jarrow and Protter [2004], where the supply function $S^{\epsilon}(s,\nu)$ depends on a parameter $\epsilon\geq 0$ with $S^0(s,\nu)=s$ corresponding to the perfect liquid situation. Using the PDE characterization of \c{C}etin, 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.

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Dylan Possamaï, Nizar Touzi, H. Mete Soner. 2012-08-18. Large liquidity expansion of super-hedging costs. https://doi.org/10.3233/asy-2011-1089

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