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Dynamic Hedging in Incomplete Markets: A Simple Solution

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  • Suleyman Basak
  • Georgy Chabakauri

Abstract

We provide fully analytical, optimal dynamic hedges in incomplete markets by employing the traditional minimum-variance criterion. Our hedges are in terms of generalized "Greeks" and naturally extend no-arbitrage--based risk management in complete markets to incomplete markets. Whereas the literature characterizes either minimum-variance static, myopic, or dynamic hedges from which a hedger may deviate unless able to precommit, our hedges are time-consistent. We apply our results to derivatives replication with infrequent trading and determine hedges and replication values, which reduce to generalized Black-Scholes expressions in specific settings. We also investigate dynamic hedging with jumps, stochastic correlation, and portfolio management with benchmarking. The Author 2012. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com., Oxford University Press.

Suggested Citation

  • Suleyman Basak & Georgy Chabakauri, 2012. "Dynamic Hedging in Incomplete Markets: A Simple Solution," The Review of Financial Studies, Society for Financial Studies, vol. 25(6), pages 1845-1896.
    • Handle: RePEc:oup:rfinst:v:25:y:2012:i:6:p:1845-1896
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    Cited by:

    1. Atmaz, Adem & Basak, Suleyman, 2019. "Option prices and costly short-selling," Journal of Financial Economics, Elsevier, vol. 134(1), pages 1-28.
    2. PeiLin Hsieh & Robert Jarrow, 2019. "Volatility Uncertainty, Time Decay, and Option Bid-Ask Spreads in an Incomplete Market," Management Science, INFORMS, vol. 65(4), pages 1833-1854, April.
    3. Paskalis Glabadanidis & Leon Zolotoy, 2013. "Benchmark replication portfolio strategies," Journal of Asset Management, Palgrave Macmillan, vol. 14(2), pages 95-110, April.
    4. Fu, Ruonan, 2025. "Essays on Ambiguity, Market Incompleteness, and Asset Pricing," Other publications TiSEM 5aac93d9-052e-4db2-a7e7-9, Tilburg University, School of Economics and Management.
    5. Ankirchner, Stefan & Schneider, Judith C. & Schweizer, Nikolaus, 2014. "Cross-hedging minimum return guarantees: Basis and liquidity risks," Journal of Economic Dynamics and Control, Elsevier, vol. 41(C), pages 93-109.
    6. Kamma, Thijs & Pelsser, Antoon, 2022. "Near-optimal asset allocation in financial markets with trading constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 766-781.
    7. Alexandre Carbonneau & Fr'ed'eric Godin, 2021. "Deep Equal Risk Pricing of Financial Derivatives with Multiple Hedging Instruments," Papers 2102.12694, arXiv.org.
    8. Cristian Ionescu, 2012. "Incomplete Markets and Financial Instability. The Role of Information," Annals of the University of Petrosani, Economics, University of Petrosani, Romania, vol. 12(1), pages 141-150.
    9. Augustyniak, Maciej & Badescu, Alexandru & Bégin, Jean-François, 2023. "A discrete-time hedging framework with multiple factors and fat tails: On what matters," Journal of Econometrics, Elsevier, vol. 232(2), pages 416-444.
    10. Dilip B. Madan & Yazid M. Sharaiha, 2015. "Option overlay strategies," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1175-1190, July.
    11. Tak Kuen Siu & Robert J. Elliott, 2019. "Hedging Options In A Doubly Markov-Modulated Financial Market Via Stochastic Flows," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-41, December.
    12. Badescu, Alexandru & Elliott, Robert J. & Ortega, Juan-Pablo, 2014. "Quadratic hedging schemes for non-Gaussian GARCH models," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 13-32.
    13. Luo, Rui & Fortenbery, T. Randall, 2016. "Corporate Hedging In Incomplete Markets: A Solution Under Price Transmission," 2016 Annual Meeting, July 31-August 2, Boston, Massachusetts 235444, Agricultural and Applied Economics Association.
    14. Ouzan, Samuel & Six, Pierre, 2025. "The demand for hedging of oil producers: A tale of risk and regret," European Journal of Operational Research, Elsevier, vol. 321(1), pages 330-343.
    15. Aivaliotis, Georgios & Palczewski, Jan, 2014. "Investment strategies and compensation of a mean–variance optimizing fund manager," European Journal of Operational Research, Elsevier, vol. 234(2), pages 561-570.
    16. Alexandru Badescu & Robert J. Elliott & Juan-Pablo Ortega, 2012. "Quadratic hedging schemes for non-Gaussian GARCH models," Papers 1209.5976, arXiv.org, revised Dec 2013.
    17. Luo, Rui & Fortenbery, T. Randall, 2017. "Corporate Hedging In Incomplete Markets: A Solution Under Price Transmission," 2017 Conference, April 24-25, 2017, St. Louis, Missouri 285879, NCR-134/ NCCC-134 Applied Commodity Price Analysis, Forecasting, and Market Risk Management.
    18. Min Dai & Hanqing Jin & Steven Kou & Yuhong Xu, 2021. "A Dynamic Mean-Variance Analysis for Log Returns," Management Science, INFORMS, vol. 67(2), pages 1093-1108, February.
    19. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    20. Niu, Baozhuang & Chu, Lap-Keung & Ni, Jian & Wang, Junwei, 2018. "Buy now and price later: Supply contracts with time-consistent mean–variance financial hedgingAuthor-Name: Li, Qiang," European Journal of Operational Research, Elsevier, vol. 268(2), pages 582-595.
    21. Lioui, Abraham, 2013. "Time consistent vs. time inconsistent dynamic asset allocation: Some utility cost calculations for mean variance preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 37(5), pages 1066-1096.
    22. Simon Scheidegger & Adrien Treccani, 2021. "Pricing American Options under High-Dimensional Models with Recursive Adaptive Sparse Expectations [Telling from Discrete Data Whether the Underlying Continuous-Time Model Is a Diffusion]," Journal of Financial Econometrics, Oxford University Press, vol. 19(2), pages 258-290.
    23. Xianhua Peng & Xiang Zhou & Bo Xiao & Yi Wu, 2024. "A Risk Sensitive Contract-unified Reinforcement Learning Approach for Option Hedging," Papers 2411.09659, arXiv.org.
    24. Alavi Fard, Farzad & He, Jian & Ivanov, Dmitry & Jie, Ferry, 2019. "A utility adjusted newsvendor model with stochastic demand," International Journal of Production Economics, Elsevier, vol. 211(C), pages 154-165.

    More about this item

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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