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A Further Study of the Choice Between Two Hedging Strategies–the Continuous Case

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  • Liang Hong

    (Robert Morris University)

Abstract

In our previous work, the choice between two popular hedging strategies was studied under the assumption that the hedge position of the underlying portfolio follows a discrete-time Markov chain with boundary conditions. This paper aims to investigate the same problem for the continuous case. We first assume that the underlying hedge position follows an arbitrary continuous-time Markov process; we give the general formulas for long-run cost per unit time under two cost structures: (1) a fixed transaction cost (2) a non-fixed transaction cost. Then we consider the case where the underlying hedge position follows a Brownian motion with drift; we show that (i) re-balancing the hedge position to the initial position is always more cost-efficient than re-balancing it to the boundary for a fixed transaction cost; (ii) when the cost function satisfies certain conditions, re-balancing the hedge position to the initial position is more cost-efficient than re-balancing it to the boundary for a non-fixed transaction cost.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:4:d:10.1007_s11009-017-9604-1
    DOI: 10.1007/s11009-017-9604-1
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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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