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Dynamic hedging of conditional value-at-risk

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  • Melnikov, Alexander
  • Smirnov, Ivan

Abstract

In this paper, the problem of partial hedging is studied by constructing hedging strategies that minimize conditional value-at-risk (CVaR) of the portfolio. Two dual versions of the problem are considered: minimization of CVaR with the initial wealth bounded from above, and minimization of hedging costs subject to a CVaR constraint. The Neyman–Pearson lemma approach is used to deduce semi-explicit solutions. Our results are illustrated by constructing CVaR-efficient hedging strategies for a call option in the Black–Scholes model and also for an embedded call option in an equity-linked life insurance contract.

Suggested Citation

  • Melnikov, Alexander & Smirnov, Ivan, 2012. "Dynamic hedging of conditional value-at-risk," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 182-190.
    • Handle: RePEc:eee:insuma:v:51:y:2012:i:1:p:182-190
    DOI: 10.1016/j.insmatheco.2012.03.011
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    References listed on IDEAS

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    Cited by:

    1. Compare, M. & Martini, F. & Zio, E., 2015. "Genetic algorithms for condition-based maintenance optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 244(2), pages 611-623.
    2. Feng, Runhuan & Shimizu, Yasutaka, 2016. "Applications of central limit theorems for equity-linked insurance," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 138-148.
    3. Barski Michał, 2016. "On the shortfall risk control: A refinement of the quantile hedging method," Statistics & Risk Modeling, De Gruyter, vol. 32(2), pages 125-141, March.
    4. Pascal Franc{c}ois & Genevi`eve Gauthier & Fr'ed'eric Godin & Carlos Octavio P'erez Mendoza, 2024. "Enhancing Deep Hedging of Options with Implied Volatility Surface Feedback Information," Papers 2407.21138, arXiv.org.
    5. Alexander Melnikov & Hongxi Wan, 2021. "On modifications of the Bachelier model," Annals of Finance, Springer, vol. 17(2), pages 187-214, June.
    6. Peng, Cheng & Li, Shuang & Zhao, Yanlong & Bao, Ying, 2021. "Sample average approximation of CVaR-based hedging problem with a deep-learning solution," The North American Journal of Economics and Finance, Elsevier, vol. 56(C).
    7. Maciej J. Capi'nski, 2014. "Hedging Conditional Value at Risk with Options," Papers 1408.6673, arXiv.org, revised Apr 2015.
    8. Nikolay A. Andreev, 2015. "Worst-Case Approach To Strategic Optimal Portfolio Selection Under Transaction Costs And Trading Limits," HSE Working papers WP BRP 45/FE/2015, National Research University Higher School of Economics.
    9. F. Godin, 2016. "Minimizing CVaR in global dynamic hedging with transaction costs," Quantitative Finance, Taylor & Francis Journals, vol. 16(3), pages 461-475, March.
    10. Jing Li & Mingxin Xu, 2013. "Optimal Dynamic Portfolio with Mean-CVaR Criterion," Risks, MDPI, vol. 1(3), pages 1-29, November.
    11. Capiński, Maciej J., 2015. "Hedging Conditional Value at Risk with options," European Journal of Operational Research, Elsevier, vol. 242(2), pages 688-691.
    12. Alexandre Carbonneau & Fr'ed'eric Godin, 2021. "Deep equal risk pricing of financial derivatives with non-translation invariant risk measures," Papers 2107.11340, arXiv.org.

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    More about this item

    Keywords

    IB10; IM01; IM10; IM53; Conditional value-at-risk; Dynamic hedging; Stochastic modeling; Quantile hedging; Unit-linked contracts;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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