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Exercise Strategies for American Exotic Options under Ambiguity

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Author Info

  • Tatjana Chudjakow

    (Institute of Mathematical Economics, Bielefeld University)

  • Jörg Vorbrink

    (Institute of Mathematical Economics, Bielefeld University)

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    Abstract

    We analyze several exotic options of American style in a multiple prior setting and study the optimal exercise strategy from the perspective of an ambiguity averse buyer in a discrete time model of Cox–Ross–Rubinstein style. The multiple prior model relaxes the assumption of a known distribution of the stock price process and takes into account decision maker’s inability to completely determine the underlying asset’s price dynamics. In order to evaluate the American option the decision maker needs to solve a stopping problem. Unlike the classical approach ambiguity averse decision maker uses a class of measures to evaluate her expected payoffs instead of a unique prior. Given time-consistency of the set of priors an appropriate version of backward induction leads to the solution as in the classical case. Using a duality result the multiple prior stopping problem can be related to the classical stopping problem for a certain probability measure – the worst-case measure. Therefore, the problem can be reduced to identifying the worst-case measure. We obtain the form of the worstcase measure for different classes of exotic options explicitly exploiting the observation that the options can be decomposed in simpler event-driven claims.

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    File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-421.pdf
    File Function: First version, 2009
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    Bibliographic Info

    Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 421.

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    Length: 40 pages
    Date of creation: Aug 2009
    Date of revision:
    Handle: RePEc:bie:wpaper:421

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    Keywords: American option; optimal stopping; ambiguity; uncertainty aversion;

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    1. Zengjing Chen & Larry G. Epstein, 2000. "Ambiguity, risk and asset returns in continuous time," RCER Working Papers 474, University of Rochester - Center for Economic Research (RCER).
    2. Frank Riedel, 2009. "Optimal Stopping With Multiple Priors," Econometrica, Econometric Society, vol. 77(3), pages 857-908, 05.
    3. Nishimura, Kiyohiko G. & Ozaki, Hiroyuki, 2007. "Irreversible investment and Knightian uncertainty," Journal of Economic Theory, Elsevier, vol. 136(1), pages 668-694, September.
    4. Ioannis Karatzas & (*), S. G. Kou, 1998. "Hedging American contingent claims with constrained portfolios," Finance and Stochastics, Springer, vol. 2(3), pages 215-258.
    5. K. Sandmann & Reimer, M., 1995. "A Discrete Time Approach for European and American Barrier Options," Discussion Paper Serie B 272, University of Bonn, Germany.
    6. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
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