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Hedging Errors Induced by Discrete Trading Under an Adaptive Trading Strategy

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  • Mats Brod'en
  • Magnus Wiktorsson

Abstract

Discrete time hedging in a complete diffusion market is considered. The hedge portfolio is rebalanced when the absolute difference between delta of the hedge portfolio and the derivative contract reaches a threshold level. The rate of convergence of the expected squared hedging error as the threshold level approaches zero is analyzed. The results hinge to a great extent on a theorem stating that the difference between the hedge ratios normalized by the threshold level tends to a triangular distribution as the threshold level tends to zero.

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  • Mats Brod'en & Magnus Wiktorsson, 2010. "Hedging Errors Induced by Discrete Trading Under an Adaptive Trading Strategy," Papers 1004.4526, arXiv.org.
    • Handle: RePEc:arx:papers:1004.4526
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    References listed on IDEAS

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    1. Takaki Hayashi & Per A. Mykland, 2005. "Evaluating Hedging Errors: An Asymptotic Approach," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 309-343, April.
    2. Geiss, Christel & Geiss, Stefan, 2006. "On an approximation problem for stochastic integrals where random time nets do not help," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 407-422, March.
    3. Emmanuel Temam & Emmanuel Gobet, 2001. "Discrete time hedging errors for options with irregular payoffs," Finance and Stochastics, Springer, vol. 5(3), pages 357-367.
    4. Tankov, Peter & Voltchkova, Ekaterina, 2009. "Asymptotic analysis of hedging errors in models with jumps," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 2004-2027, June.
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