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Maximum Drawdown Insurance

Author

Listed:
  • PETER CARR

    (Courant Institute, NYU, 251 Mercer Street, New York, New York 10012, USA)

  • HONGZHONG ZHANG

    (Department of Statistics, Columbia University, 1255 Amsterdam Avenue, New York, New York 10027, USA)

  • OLYMPIA HADJILIADIS

    (Department of Mathematics, Brooklyn College and the Graduate Center, CUNY, New York, New York 10016, USA)

Abstract

The drawdown of an asset is a risk measure defined in terms of the running maximum of the asset's spot price over some period [0, T]. The asset price is said to have drawn down by at least $K over this period if there exists a time at which the underlying is at least $K below its maximum-to-date. We introduce insurance against a large realization of maximum drawdown and a novel way to hedge the liability incurred by underwriting this insurance. Our proposed insurance pays a fixed amount should the maximum drawdown exceed some fixed threshold over a specified period. The need for this drawdown insurance would diminish should markets rise before they fall. Consequently, we propose a second kind of cheaper maximum drawdown insurance that pays a fixed amount contingent on the drawdown preceding a drawup. We propose double barrier options as hedges for both kinds of insurance against large maximum drawdowns. In fact for the second kind of insurance we show that the hedge is model-free. Since double barrier options do not trade liquidly in all markets, we examine the assumptions under which alternative hedges using either single barrier options or standard vanilla options can be used.

Suggested Citation

  • Peter Carr & Hongzhong Zhang & Olympia Hadjiliadis, 2011. "Maximum Drawdown Insurance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(08), pages 1195-1230.
    • Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:08:n:s0219024911006826
    DOI: 10.1142/S0219024911006826
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    Citations

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    Cited by:

    1. Jorge González Cázares & Aleksandar Mijatović, 2022. "Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximation," Finance and Stochastics, Springer, vol. 26(4), pages 671-732, October.
    2. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, August.
    3. 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).
    4. Ola Mahmoud, 2015. "The Temporal Dimension of Risk," Papers 1501.01573, arXiv.org, revised Jun 2016.
    5. 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.
    6. Li, Shu & Zhou, Xiaowen, 2022. "The Parisian and ultimate drawdowns of Lévy insurance models," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 140-160.
    7. Zbigniew Palmowski & Joanna Tumilewicz, 2017. "Pricing insurance drawdown-type contracts with underlying L\'evy assets," Papers 1701.01891, arXiv.org, revised Oct 2017.
    8. 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.
    9. David Landriault & Bin Li & Hongzhong Zhang, 2014. "On the Frequency of Drawdowns for Brownian Motion Processes," Papers 1403.1183, arXiv.org.
    10. Tommaso Proietti, 2024. "Ups and (Draw)Downs," CEIS Research Paper 576, Tor Vergata University, CEIS, revised 03 May 2024.
    11. David Landriault & Bin Li & Hongzhong Zhang, 2015. "On magnitude, asymptotics and duration of drawdowns for L\'{e}vy models," Papers 1506.08408, arXiv.org, revised Sep 2016.
    12. 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.
    13. 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.
    14. Emiel Lemahieu & Kris Boudt & Maarten Wyns, 2023. "Generating drawdown-realistic financial price paths using path signatures," Papers 2309.04507, arXiv.org.
    15. 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.
    16. Baurdoux, Erik J. & Palmowski, Z & Pistorius, Martijn R, 2017. "On future drawdowns of Lévy processes," LSE Research Online Documents on Economics 84342, London School of Economics and Political Science, LSE Library.
    17. Tian, Miao & Yang, Xiangfeng & Zhang, Yi, 2019. "Barrier option pricing of mean-reverting stock model in uncertain environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 126-143.
    18. Goldberg, Lisa R & Mouti, Saad, 2022. "Sustainable investing and the cross-section of returns and maximum drawdown," Department of Economics, Working Paper Series qt98f9410b, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    19. Marcos Escobar & Peter Hieber & Matthias Scherer, 2014. "Efficiently pricing double barrier derivatives in stochastic volatility models," Review of Derivatives Research, Springer, vol. 17(2), pages 191-216, July.
    20. 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.
    21. David Landriault & Bin Li & Hongzhong Zhang, 2017. "A Unified Approach for Drawdown (Drawup) of Time-Homogeneous Markov Processes," Papers 1702.07786, arXiv.org.
    22. Jorge Ignacio Gonz'alez C'azares & Aleksandar Mijatovi'c, 2021. "Monte Carlo algorithm for the extrema of tempered stable processes," Papers 2103.15310, arXiv.org, revised Dec 2022.
    23. Angelos Dassios & Jia Wei Lim, 2018. "An Efficient Algorithm for Simulating the Drawdown Stopping Time and the Running Maximum of a Brownian Motion," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 189-204, March.
    24. Damiano Rossello & Silvestro Lo Cascio, 2021. "A refined measure of conditional maximum drawdown," Risk Management, Palgrave Macmillan, vol. 23(4), pages 301-321, December.

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