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On the computation of hedging strategies in affine GARCH models

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  • Maciej Augustyniak
  • Alexandru Badescu

Abstract

This paper discusses the computation of hedging strategies under affine Gaussian GARCH dynamics. The risk‐minimization hedging strategy is derived in closed‐form and related to minimum variance delta hedging. Several numerical experiments are conducted to investigate the accuracy and properties of the proposed hedging formula, as well as the convergence to its continuous‐time counterpart based on the GARCH diffusion limit process. An empirical analysis with S&P 500 option data over 2001–2015 indicates that risk‐minimization hedging with the affine Gaussian GARCH model outperforms benchmark delta hedges. Our study also reveals that the variance‐dependent pricing kernel contributes to improving the hedging performance.

Suggested Citation

  • Maciej Augustyniak & Alexandru Badescu, 2021. "On the computation of hedging strategies in affine GARCH models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(5), pages 710-735, May.
    • Handle: RePEc:wly:jfutmk:v:41:y:2021:i:5:p:710-735
    DOI: 10.1002/fut.22187
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    1. J.L. Prigent & O. Scaillet, 2000. "Weak Convergence of Hedging Strategies of Contingent Claims," THEMA Working Papers 2000-50, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    2. Martin Schweizer, 1995. "Variance-Optimal Hedging in Discrete Time," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 1-32, February.
    3. Peter Christoffersen & Steven Heston & Kris Jacobs, 2013. "Capturing Option Anomalies with a Variance-Dependent Pricing Kernel," Review of Financial Studies, Society for Financial Studies, vol. 26(8), pages 1963-2006.
    4. Maciej Augustyniak & Frédéric Godin & Clarence Simard, 2017. "Assessing the effectiveness of local and global quadratic hedging under GARCH models," Quantitative Finance, Taylor & Francis Journals, vol. 17(9), pages 1305-1318, September.
    5. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    6. François, Pascal & Gauthier, Geneviève & Godin, Frédéric, 2014. "Optimal hedging when the underlying asset follows a regime-switching Markov process," European Journal of Operational Research, Elsevier, vol. 237(1), pages 312-322.
    7. Peter Christoffersen & Redouane Elkamhi & Bruno Feunou & Kris Jacobs, 2010. "Option Valuation with Conditional Heteroskedasticity and Nonnormality," The Review of Financial Studies, Society for Financial Studies, vol. 23(5), pages 2139-2183.
    8. René Garcia & Èric Renault, 1998. "A Note on Hedging in ARCH and Stochastic Volatility Option Pricing Models," Mathematical Finance, Wiley Blackwell, vol. 8(2), pages 153-161, April.
    9. Alan L. Lewis, 2001. "A Simple Option Formula for General Jump-Diffusion and other Exponential Levy Processes," Related articles explevy, Finance Press.
    10. Alexandru Badescu & Zhenyu Cui & Juan-Pablo Ortega, 2019. "Closed-form variance swap prices under general affine GARCH models and their continuous-time limits," Annals of Operations Research, Springer, vol. 282(1), pages 27-57, November.
    11. Friedrich Hubalek & Jan Kallsen & Leszek Krawczyk, 2006. "Variance-optimal hedging for processes with stationary independent increments," Papers math/0607112, arXiv.org.
    12. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    13. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
    14. Schweizer, Martin, 1991. "Option hedging for semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 339-363, April.
    15. Juan-Pablo Ortega, 2012. "GARCH options via local risk minimization," Quantitative Finance, Taylor & Francis Journals, vol. 12(7), pages 1095-1110, May.
    16. Rolf Poulsen & Klaus Reiner Schenk-Hoppe & Christian-Oliver Ewald, 2009. "Risk minimization in stochastic volatility models: model risk and empirical performance," Quantitative Finance, Taylor & Francis Journals, vol. 9(6), pages 693-704.
    17. Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1998. "Implied Volatility Functions: Empirical Tests," Journal of Finance, American Finance Association, vol. 53(6), pages 2059-2106, December.
    18. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
    19. Alexandru Badescu & Zhenyu Cui & Juan-Pablo Ortega, 2017. "Non-affine GARCH Option Pricing Models, Variance-Dependent Kernels, and Diffusion Limits," Journal of Financial Econometrics, Oxford University Press, vol. 15(4), pages 602-648.
    20. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    21. Hull, John & White, Alan, 2017. "Optimal delta hedging for options," Journal of Banking & Finance, Elsevier, vol. 82(C), pages 180-190.
    22. Bruno R�millard & Sylvain Rubenthaler, 2013. "Optimal hedging in discrete time," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 819-825, May.
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    Cited by:

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    2. Wang, Xingchun & Zhang, Han, 2022. "Pricing basket spread options with default risk under Heston–Nandi GARCH models," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    3. 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.

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