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Martingale Approach To Pricing Perpetual American Options On Two Stocks

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  • Hans U. Gerber
  • Hlias S. W. Shiu
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    Abstract

    We study the pricing of American options on two stocks without expiration date and with payoff functions which are positively homogeneous with respect to the two stock prices. Examples of such options are the perpetuai Margrabe option, whose payoff is the amount by which one stock outperforms the other, and the perpetual maximum option, whose payoff is the maximum of the two stock prices Our approach to pricing such options is to take advantage of their stationary nature and apply the optional sampling theorem to two martingales constructed with respect to the risk-neutral measure the optimal exercise boundaries, which do not vary with respect to the time variable, are determined by the smooth pasting or high contact condition the martingale approach avoids the use of differential equations. Copyright 1996 Blackwell Publishers.

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    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Mathematical Finance.

    Volume (Year): 6 (1996)
    Issue (Month): 3 ()
    Pages: 303-322

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    Handle: RePEc:bla:mathfi:v:6:y:1996:i:3:p:303-322

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    Cited by:
    1. Sheldon Lin, X., 1998. "Double barrier hitting time distributions with applications to exotic options," Insurance: Mathematics and Economics, Elsevier, vol. 23(1), pages 45-58, October.
    2. CHESNEY, Marc & LOUBERGE, Henri & VILLENEUVE, Stéphane, 2001. "Long-term risk management of nuclear waste : a real options approach," Les Cahiers de Recherche 767, HEC Paris.
    3. Min Dai & Zuo Quan Xu, 2009. "Optimal Redeeming Strategy of Stock Loans," Papers 0906.0702, arXiv.org.
    4. Ernst Eberlein & Antonis Papapantoleon & Albert N. Shiryaev, 2008. "Esscher transform and the duality principle for multidimensional semimartingales," Papers 0809.0301, arXiv.org, revised Nov 2009.
    5. Gerber, Hans U. & Shiu, Elias S. W., 1996. "Actuarial bridges to dynamic hedging and option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 18(3), pages 183-218, November.
    6. Shuqing Jiang & Zongxia Liang & Weiming Wu, 2010. "Stock loan with Automatic termination clause, cap and margin," Papers 1005.1357, arXiv.org, revised Sep 2010.
    7. Svetlana Boyarchenko & Sergei Levendorskii, 2004. "American options: the EPV pricing model," Finance 0405024, EconWPA.
    8. Fajardo, J. & Mordeckiz, E., 2004. "Duality and Derivative Pricing with Lévy Processes," Finance Lab Working Papers flwp_71, Finance Lab, Insper Instituto de Ensino e Pesquisa.
    9. Fajardo, J. & Mordeckiy, E., 2003. "Pricing Derivatives on Two Lévy-driven Stocks," Finance Lab Working Papers flwp_56, Finance Lab, Insper Instituto de Ensino e Pesquisa.
    10. Boyle, Phelim P. & Lin, X. Sheldon, 1997. "Bounds on contingent claims based on several assets," Journal of Financial Economics, Elsevier, vol. 46(3), pages 383-400, December.

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