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On the choice between two delta-hedging strategies

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  • Liang Hong

    (Robert Morris University)

Abstract

This paper studies the choice between two popular hedging strategies by assuming that the hedge position (delta) follows a Markov chain with boundary conditions. We give the formula for long-run cost per unit time under two different cost structures: (I) a fixed transaction cost and (II) a non-fixed transaction cost. Then, we consider the case where the hedge position follows a random walk; we show that (i) re-balancing delta to the initial position is always more cost-efficient than re-balancing it to the edge for a fixed transaction cost; (ii) under certain conditions, re-balancing delta to the initial position is less cost-efficient than re-balancing it to the edge for a non-fixed transaction cost. In addition, we quantify the magnitude of the efficiency in both cases.

Suggested Citation

  • Liang Hong, 2016. "On the choice between two delta-hedging strategies," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(1), pages 69-80, April.
    • Handle: RePEc:spr:decfin:v:39:y:2016:i:1:d:10.1007_s10203-016-0172-6
    DOI: 10.1007/s10203-016-0172-6
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    References listed on IDEAS

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    1. T. F. Coleman & Y. Kim & Y. Li & M. Patron, 2007. "Robustly Hedging Variable Annuities With Guarantees Under Jump and Volatility Risks," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(2), pages 347-376, June.
    2. Coleman, Thomas F. & Li, Yuying & Patron, Maria-Cristina, 2006. "Hedging guarantees in variable annuities under both equity and interest rate risks," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 215-228, April.
    3. Kling, Alexander & Ruez, Frederik & Ruß, Jochen, 2011. "The Impact of Stochastic Volatility on Pricing, Hedging, and Hedge Efficiency of Withdrawal Benefit Guarantees in Variable Annuities," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 511-545, November.
    4. Min Dai & Yue Kuen Kwok & Jianping Zong, 2008. "Guaranteed Minimum Withdrawal Benefit In Variable Annuities," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 595-611, October.
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    Cited by:

    1. Liang Hong, 2018. "A Further Study of the Choice Between Two Hedging Strategies–the Continuous Case," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1189-1198, December.

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    More about this item

    Keywords

    Cost of hedging; Re-balancing; Markov chain; Random walk; Fixed transaction cost; Non-fixed transaction cost;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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