# Large liquidity expansion of super-hedging costs

## Author Info

Listed author(s):
• Dylan Possama\"i
• Nizar Touzi
• H. Mete Soner
Registered author(s):

## 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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File URL: http://arxiv.org/pdf/1208.3785

## Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1208.3785.

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 Length: Date of creation: Aug 2012 Date of revision: Apr 2015 Publication status: Published in Asymptotic Analysis, 79(1-2), 2012, 45-64 Handle: RePEc:arx:papers:1208.3785 Contact details of provider: Web page: http://arxiv.org/

## References

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1. Umut Çetin & L. C. G. Rogers, 2007. "Modeling Liquidity Effects In Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 15-29.
2. U. Çetin & R. Jarrow & P. Protter & M. Warachka, 2008. "Pricing Options in an Extended Black Scholes Economy with Illiquidity: Theory and Empirical Evidence," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 9, pages 185-221 World Scientific Publishing Co. Pte. Ltd..
3. Umut Çetin & Robert A. Jarrow & Philip Protter, 2008. "Liquidity risk and arbitrage pricing theory," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 8, pages 153-183 World Scientific Publishing Co. Pte. Ltd..
4. Halil Mete Soner & Guy Barles, 1998. "Option pricing with transaction costs and a nonlinear Black-Scholes equation," Finance and Stochastics, Springer, vol. 2(4), pages 369-397.
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