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Asymptotically optimal discretization of hedging strategies with jumps

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  • Mathieu Rosenbaum
  • Peter Tankov

Abstract

In this work, we consider the hedging error due to discrete trading in models with jumps. Extending an approach developed by Fukasawa [In Stochastic Analysis with Financial Applications (2011) 331-346 Birkh\"{a}user/Springer Basel AG] for continuous processes, we propose a framework enabling us to (asymptotically) optimize the discretization times. More precisely, a discretization rule is said to be optimal if for a given cost function, no strategy has (asymptotically, for large cost) a lower mean square discretization error for a smaller cost. We focus on discretization rules based on hitting times and give explicit expressions for the optimal rules within this class.

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File URL: http://arxiv.org/pdf/1108.5940
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1108.5940.

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Date of creation: Aug 2011
Date of revision: Apr 2014
Publication status: Published in Annals of Applied Probability 2014, Vol. 24, No. 3, 1002-1048
Handle: RePEc:arx:papers:1108.5940

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  1. Rosenbaum, Mathieu & Tankov, Peter, 2011. "Asymptotic results for time-changed Lévy processes sampled at hitting times," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 121(7), pages 1607-1632, July.
  2. Mats Brodén & Peter Tankov, 2011. "Tracking Errors From Discrete Hedging In Exponential Lévy Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 803-837.
  3. Ale\v{s} \v{C}ern\'y & Jan Kallsen, 2007. "On the structure of general mean-variance hedging strategies," Papers 0708.1715, arXiv.org.
  4. Friedrich Hubalek & Jan Kallsen & Leszek Krawczyk, 2006. "Variance-optimal hedging for processes with stationary independent increments," Papers math/0607112, arXiv.org.
  5. Bertsimas, Dimitris & Kogan, Leonid & Lo, Andrew W., 2000. "When is time continuous?," Journal of Financial Economics, Elsevier, Elsevier, vol. 55(2), pages 173-204, February.
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Cited by:
  1. Christoph K\"uhn & Johannes Muhle-Karbe, 2013. "Optimal Liquidity Provision in Limit Order Markets," Papers 1309.5235, arXiv.org, revised May 2014.
  2. Albert Altarovici & Johannes Muhle-Karbe & H. Mete Soner, 2013. "Asymptotics for Fixed Transaction Costs," Papers 1306.2802, arXiv.org, revised Oct 2013.

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