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Portfolio sensitivity to changes in the maximum and the maximum drawdown

Author

Listed:
  • Libor Pospisil
  • Jan Vecer

Abstract

In this article, we define new 'Greeks' for financial derivatives: sensitivities to the running maximum and the running maximum drawdown of an underlying asset. Some types of portfolios, such as the net asset value of a hedge fund or performance fees, are sensitive to these parameters. In order to illustrate the concept of the new 'Greeks', we derive probabilistic representations of sensitivities for two classes of financial contracts: forwards on the maximum drawdown and lookback options. These results allow us to interpret the delta-hedge of the contracts in a novel way.

Suggested Citation

  • Libor Pospisil & Jan Vecer, 2010. "Portfolio sensitivity to changes in the maximum and the maximum drawdown," Quantitative Finance, Taylor & Francis Journals, vol. 10(6), pages 617-627.
  • Handle: RePEc:taf:quantf:v:10:y:2010:i:6:p:617-627
    DOI: 10.1080/14697680903008751
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    References listed on IDEAS

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    1. Goldman, M Barry & Sosin, Howard B & Gatto, Mary Ann, 1979. "Path Dependent Options: "Buy at the Low, Sell at the High"," Journal of Finance, American Finance Association, vol. 34(5), pages 1111-1127, December.
    2. David G. Hobson, 1998. "Robust hedging of the lookback option," Finance and Stochastics, Springer, vol. 2(4), pages 329-347.
    3. Eberlein, Ernst & Papapantoleon, Antonis, 2005. "Equivalence of floating and fixed strike Asian and lookback options," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 31-40, January.
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    Cited by:

    1. repec:eee:insuma:v:79:y:2018:i:c:p:1-14 is not listed on IDEAS
    2. Ola Mahmoud, 2015. "The Temporal Dimension of Risk," Papers 1501.01573, arXiv.org, revised Jun 2016.
    3. Zbigniew Palmowski & Joanna Tumilewicz, 2017. "Fair valuation of L\'evy-type drawdown-drawup contracts with general insured and penalty functions," Papers 1712.04418, arXiv.org, revised Feb 2018.
    4. Vladimir Cherny & Jan Obłój, 2013. "Portfolio optimisation under non-linear drawdown constraints in a semimartingale financial model," Finance and Stochastics, Springer, vol. 17(4), pages 771-800, October.
    5. Zbigniew Palmowski & Joanna Tumilewicz, 2017. "Pricing insurance drawdown-type contracts with underlying L\'evy assets," Papers 1701.01891, arXiv.org, revised Oct 2017.
    6. David Landriault & Bin Li & Hongzhong Zhang, 2014. "On the Frequency of Drawdowns for Brownian Motion Processes," Papers 1403.1183, arXiv.org.
    7. repec:eee:finlet:v:22:y:2017:i:c:p:95-100 is not listed on IDEAS
    8. Landriault, David & Li, Bin & Li, Shu, 2015. "Analysis of a drawdown-based regime-switching Lévy insurance model," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 98-107.
    9. Zhang, Hongzhong & Leung, Tim & Hadjiliadis, Olympia, 2013. "Stochastic modeling and fair valuation of drawdown insurance," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 840-850.
    10. Magnus, Jan R. & Vasnev, Andrey L., 2015. "Interpretation and use of sensitivity in econometrics, illustrated with forecast combinations," International Journal of Forecasting, Elsevier, vol. 31(3), pages 769-781.

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