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

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Author Info
Leonel Pérez-Hernández () (School of Economics, Universidad de Guanajuato)

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Abstract

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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Paper provided by Universidad de Guanajuato in its series School of Economics Working Papers with number EC200505.

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Handle: RePEc:gua:wpaper:ec200505

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Related research
Keywords: Partial Hedging; Efficient Hedging; Expected Loss; American Claims; Incomplete Markets; Dynamic Measures of Risk.;

Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
G19 - Financial Economics - - General Financial Markets - - - Other

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  1. Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146. [Downloadable!] (restricted)
  2. Ernst Eberlein & Jean Jacod, 1997. "On the range of options prices (*)," Finance and Stochastics, Springer, vol. 1(2), pages 131-140. [Downloadable!] (restricted)
  3. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. Ioannis Karatzas & Jaksa Cvitanic, 1999. "On dynamic measures of risk," Finance and Stochastics, Springer, vol. 3(4), pages 451-482. [Downloadable!] (restricted)
  6. Paolo Guasoni, 2002. "Risk minimization under transaction costs," Finance and Stochastics, Springer, vol. 6(1), pages 91-113. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. Yumiharu Nakano, 2003. "Minimizing coherent risk measures of shortfall in discrete-time models with cone constraints," Applied Mathematical Finance, Taylor and Francis Journals, vol. 10(2), pages 163-181, June. [Downloadable!] (restricted)
  9. N. Bellamy & M. Jeanblanc, 2000. "Incompleteness of markets driven by a mixed diffusion," Finance and Stochastics, Springer, vol. 4(2), pages 209-222. [Downloadable!] (restricted)
  10. Nakano, Yumiharu, 2004. "Minimization of shortfall risk in a jump-diffusion model," Statistics & Probability Letters, Elsevier, vol. 67(1), pages 87-95, March. [Downloadable!] (restricted)
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