Hedging through a Limit Order Book with Varying Liquidity
We relax the classical price-taking assumption and study the impact of orders of arbitrary size on price when the availability of liquidity is a concern in hedging. Our paper extends the earlier literature, suggesting that an environment with a permanent impact can be viewed as a special case with zero resilience, whereas an environment with a temporary impact can be viewed as a limit case with infinite resilience speed. Furthermore, our results hold for more general stochastic processes for the underlying asset: for example, for a generic Lévy process.
|Date of creation:||Apr 2012|
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- Aur\'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756, arXiv.org, revised Feb 2010.
- Obizhaeva, Anna A. & Wang, Jiang, 2013.
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Elsevier, vol. 16(1), pages 1-32.
- Anna Obizhaeva & Jiang Wang, 2005. "Optimal Trading Strategy and Supply/Demand Dynamics," NBER Working Papers 11444, National Bureau of Economic Research, Inc.
- Umut Çetin & H. Soner & Nizar Touzi, 2010. "Option hedging for small investors under liquidity costs," Finance and Stochastics, Springer, vol. 14(3), pages 317-341, September.
- E. Platen & M. Schweizer, 1997. "On Feedback Effects from Hedging Derivatives," SFB 373 Discussion Papers 1997,83, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Aurelien Alfonsi & Antje Fruth & Alexander Schied, 2010. "Optimal execution strategies in limit order books with general shape functions," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 143-157.
- Koichi Matsumoto, 2009. "Mean-Variance Hedging with Uncertain Trade Execution," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(3), pages 219-252.
- H. Mete Soner & Umut Cetin & Nizar Touzi, 2010. "Option hedging for small investors under liquidity costs," LSE Research Online Documents on Economics 28992, London School of Economics and Political Science, LSE Library.
- Friedrich Hubalek & Jan Kallsen & Leszek Krawczyk, 2006. "Variance-optimal hedging for processes with stationary independent increments," Papers math/0607112, arXiv.org.
- RØdiger Frey, 1998. "Perfect option hedging for a large trader," Finance and Stochastics, Springer, vol. 2(2), pages 115-141.
- Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
- 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..
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