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Variance-optimal hedging for processes with stationary independent increments

  • Friedrich Hubalek
  • Jan Kallsen
  • Leszek Krawczyk
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    We determine the variance-optimal hedge when the logarithm of the underlying price follows a process with stationary independent increments in discrete or continuous time. Although the general solution to this problem is known as backward recursion or backward stochastic differential equation, we show that for this class of processes the optimal endowment and strategy can be expressed more explicitly. The corresponding formulas involve the moment, respectively, cumulant generating function of the underlying process and a Laplace- or Fourier-type representation of the contingent claim. An example illustrates that our formulas are fast and easy to evaluate numerically.

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    File URL: http://arxiv.org/pdf/math/0607112
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    Paper provided by arXiv.org in its series Papers with number math/0607112.

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    Date of creation: Jul 2006
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    Publication status: Published in Annals of Applied Probability 2006, Vol. 16, No. 2, 853-885
    Handle: RePEc:arx:papers:math/0607112
    Contact details of provider: Web page: http://arxiv.org/

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    1. Hua He and Neil D. Pearson., 1989. "Consumption and Portfolio Policies with Incomplete Markets and Short-Sale Constraints: The Finite Dimensional Case," Research Program in Finance Working Papers RPF-189, University of California at Berkeley.
    2. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    3. Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July.
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