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Maximum Drawdown Insurance

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Author Info

  • 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)

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    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.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

    Volume (Year): 14 (2011)
    Issue (Month): 08 ()
    Pages: 1195-1230

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    Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:08:p:1195-1230

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    Related research

    Keywords: Drawdown; drawup; static replication;

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    Cited by:
    1. Hongzhong Zhang & Tim Leung & Olympia Hadjiliadis, 2013. "Stochastic Modeling and Fair Valuation of Drawdown Insurance," Science & Finance (CFM) working paper archive 1310.3860, Science & Finance, Capital Fund Management.
    2. David Landriault & Bin Li & Hongzhong Zhang, 2014. "On the Frequency of Drawdowns for Brownian Motion Processes," Science & Finance (CFM) working paper archive 1403.1183, Science & Finance, Capital Fund Management.

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