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Portfolio sensitivity to changes in the maximum and the maximum drawdown

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  • 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.
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    Cited by:

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    2. Zbigniew Palmowski & Joanna Tumilewicz, 2018. "Drawdown insurance contracts for the Lévy-type model with the phase-type jump distribution and general reward function," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 51, pages 255-270.
    3. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078.
    4. C. A. Valle & J. E. Beasley, 2019. "A nonlinear optimisation model for constructing minimal drawdown portfolios," Papers 1908.08684, arXiv.org.
    5. Zhang, Gongqiu & Li, Lingfei, 2023. "A general method for analysis and valuation of drawdown risk," Journal of Economic Dynamics and Control, Elsevier, vol. 152(C).
    6. Ola Mahmoud, 2015. "The Temporal Dimension of Risk," Papers 1501.01573, arXiv.org, revised Jun 2016.
    7. 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.
    8. Long Bai & Peng Liu, 2019. "Drawdown and Drawup for Fractional Brownian Motion with Trend," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1581-1612, September.
    9. Zbigniew Palmowski & Joanna Tumilewicz, 2017. "Pricing insurance drawdown-type contracts with underlying L\'evy assets," Papers 1701.01891, arXiv.org, revised Oct 2017.
    10. Caglar, Mine & Vardar-Acar, Ceren, 2013. "Distribution of maximum loss of fractional Brownian motion with drift," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2729-2734.
    11. Mendes, Beatriz Vaz de Melo & Lavrado, Rafael Coelho, 2017. "Implementing and testing the Maximum Drawdown at Risk," Finance Research Letters, Elsevier, vol. 22(C), pages 95-100.
    12. 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.
    13. Zhenyu Cui & Duy Nguyen, 2018. "Magnitude and Speed of Consecutive Market Crashes in a Diffusion Model," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 117-135, March.
    14. 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.
    15. Palmowski, Zbigniew & Tumilewicz, Joanna, 2018. "Pricing insurance drawdown-type contracts with underlying Lévy assets," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 1-14.
    16. Rolando Rubilar-Torrealba & Lisandro Fermin & Soledad Torres, 2025. "Modeling Maximum drawdown Records with Piecewise Deterministic Markov Processe in Capital Markets," Papers 2503.23221, arXiv.org.
    17. Landriault, David & Li, Bin & Lkabous, Mohamed Amine, 2021. "On the analysis of deep drawdowns for the Lévy insurance risk model," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 147-155.
    18. 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.
    19. David Landriault & Bin Li & Hongzhong Zhang, 2014. "On the Frequency of Drawdowns for Brownian Motion Processes," Papers 1403.1183, arXiv.org.
    20. Jaehyung Choi, 2021. "Maximum Drawdown, Recovery, and Momentum," JRFM, MDPI, vol. 14(11), pages 1-25, November.
    21. Damiano Rossello & Silvestro Lo Cascio, 2021. "A refined measure of conditional maximum drawdown," Risk Management, Palgrave Macmillan, vol. 23(4), pages 301-321, December.
    22. Pawe{l} Stc{e}pniak & Zbigniew Palmowski, 2025. "Pricing time-capped American options using Least Squares Monte Carlo method," Papers 2503.01040, arXiv.org.
    23. 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.
    24. Hongzhong Zhang & Olympia Hadjiliadis, 2012. "Drawdowns and the Speed of Market Crash," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 739-752, September.

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