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On the Existence of Efficient Hedge for an American Contingent Claim: Discrete Time Market

  • Leonel Pérez-Hernández

    ()

    (Department of Economics and Finance, Universidad de Guanajuato)

We show the existence of efficient hedge strategies for an investor facing the problem of a lack of initial capital for implementing a (super-) hedging strategy for an american contingent claim in a general incomplete market. For the optimization we consider once the maximization of the expected success ratio of the worst possible case as well as the minimization of the shortfall risk. These problems lead to stochastic games which do not need to have a value. We provide an example for this in a CRR model for an american put. Alternatively we might fix a minimal expected success ratio or a boundary for the shortfall risk and look for the minimal amount of initial capital for which there is a self-financing strategy fulfilling one or the other restriction. For all these problems we show the optimal strategy consists in hedging a modified american claim for some ``randomized test process''.

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File URL: http://economia.ugto.org/WorkingPapers/EC200505.pdf
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Paper provided by Universidad de Guanajuato, Department of Economics and Finance in its series Department of Economics and Finance Working Papers with number EC200505.

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Length: 22 pages
Date of creation: Oct 2005
Date of revision:
Publication status: Published in Quantitative Finance (2007)
Handle: RePEc:gua:wpaper:ec200505
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  1. Ernst Eberlein & Jean Jacod, 1997. "On the range of options prices (*)," Finance and Stochastics, Springer, vol. 1(2), pages 131-140.
  2. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
  3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  4. Yumiharu Nakano, 2003. "Minimizing coherent risk measures of shortfall in discrete-time models with cone constraints," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(2), pages 163-181.
  5. Jakša Cvitanić, 1999. "Methods of Partial Hedging," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 6(1), pages 7-35, January.
  6. Ioannis Karatzas & Jaksa Cvitanic, 1999. "On dynamic measures of risk," Finance and Stochastics, Springer, vol. 3(4), pages 451-482.
  7. Paolo Guasoni, 2002. "Risk minimization under transaction costs," Finance and Stochastics, Springer, vol. 6(1), pages 91-113.
  8. Marco Schulmerich & Siegfried Trautmann, 2003. "Local Expected Shortfall-Hedging in Discrete Time," Review of Finance, European Finance Association, vol. 7(1), pages 75-102.
  9. N. Bellamy & M. Jeanblanc, 2000. "Incompleteness of markets driven by a mixed diffusion," Finance and Stochastics, Springer, vol. 4(2), pages 209-222.
  10. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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