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Hedging strategies with a put option and their failure rates

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  • Guanghui Huang
  • Jing Xu
  • Wenting Xing
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    Abstract

    The problem of stock hedging is reconsidered in this paper, where a put option is chosen from a set of available put options to hedge the market risk of a stock. A formula is proposed to determine the probability that the potential loss exceeds a predetermined level of Value-at-Risk, which is used to find the optimal strike price and optimal hedge ratio. The assumptions that the chosen put option finishes in-the-money and the constraint of hedging budget is binding are relaxed in this paper. A hypothesis test is proposed to determine whether the failure rate of hedging strategy is greater than the predetermined level of risk. The performances of the proposed method and the method with those two assumptions are compared through simulations. The results of simulated investigations indicate that the proposed method is much more prudent than the method with those two assumptions.

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    File URL: http://arxiv.org/pdf/1110.0159
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1110.0159.

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    Date of creation: Oct 2011
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    Handle: RePEc:arx:papers:1110.0159

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    1. Dong-Hyun Ahn & Jacob Boudoukh & Matthew Richardson & Robert F. Whitelaw, 1999. "Optimal Risk Management Using Options," Journal of Finance, American Finance Association, American Finance Association, vol. 54(1), pages 359-375, 02.
    2. Andrew K. Prevost & Lawrence C. Rose & Gary Miller, 2000. "Derivatives Usage and Financial Risk Management in Large and Small Economies: A Comparative Analysis," Journal of Business Finance & Accounting, Wiley Blackwell, Wiley Blackwell, vol. 27(5&6), pages 733-759.
    3. René M. Stulz, 1996. "Rethinking Risk Management," Journal of Applied Corporate Finance, Morgan Stanley, Morgan Stanley, vol. 9(3), pages 8-25.
    4. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, Elsevier, vol. 26(7), pages 1443-1471, July.
    5. Sohnke M. Bartram & Gregory W. Brown & Frank R. Fehle, 2003. "International Evidence on Financial Derivatives Usage," Finance, EconWPA 0307003, EconWPA, revised 24 Jul 2003.
    6. Carlo Acerbi & Dirk Tasche, 2001. "Expected Shortfall: a natural coherent alternative to Value at Risk," Papers cond-mat/0105191, arXiv.org.
    7. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 9(3), pages 203-228.
    8. Griselda Deelstra & Michèle Vanmaele & David Vyncke, 2010. "Minimizing the Risk of a Financial Product Using a Put Option," Journal of Risk & Insurance, The American Risk and Insurance Association, The American Risk and Insurance Association, vol. 77(4), pages 767-800.
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