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Optimal partial hedging of an American option: shifting the focus to the expiration date

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  • Peter Lindberg

Abstract

As a main contribution we present a new approach for studying the problem of optimal partial hedging of an American contingent claim in a finite and complete discrete-time market. We assume that at an early exercise time the investor can borrow the amount she has to pay for the option holder by entering a short position in the numéraire asset and that this loan in turn will mature at the expiration date. We model and solve a partial hedging problem, where the investor’s purpose is to find a minimal amount at which she can hedge the above-mentioned loan with a given probability, while the potential shortfall is bounded above by a certain number of numéraire assets. A knapsack problem approach and greedy algorithm are used in solving the problem. To get a wider view of the subject and to make interesting comparisons, we treat also a closely related European case as well as an American case where a barrier condition is applied. Copyright Springer-Verlag 2012

Suggested Citation

  • Peter Lindberg, 2012. "Optimal partial hedging of an American option: shifting the focus to the expiration date," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(3), pages 221-243, June.
    • Handle: RePEc:spr:mathme:v:75:y:2012:i:3:p:221-243
    DOI: 10.1007/s00186-012-0382-9
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    References listed on IDEAS

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    1. Ioannis Karatzas & Jaksa Cvitanic, 1999. "On dynamic measures of risk," Finance and Stochastics, Springer, vol. 3(4), pages 451-482.
    2. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
    3. Leonel Perez-hernandez, 2007. "On the existence of an efficient hedge for an American contingent claim within a discrete time market," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 547-551.
    4. Peter Lindberg, 2010. "Optimal partial hedging in a discrete-time market as a knapsack problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(3), pages 433-451, December.
    5. Sabrina Mulinacci, 2011. "The efficient hedging problem for American options," Finance and Stochastics, Springer, vol. 15(2), pages 365-397, June.
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