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Numerical Comparison of Local Risk-Minimisation & Mean-Variance Hedging

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Abstract

This paper provides comparative results on prices, hedging strategies and risks for local risk-minimisation and mean-variance hedging for a class of stochastic volatility models. A pricing and hedging framework is presented for both approaches with detailed analysis undertaken for the well-known Heston and Stein/Stein stochastic volatility models. These illustrate important quantitative differences between the two approaches.

Suggested Citation

  • David Heath & Eckhard Platen & Martin Schweizer, 2001. "Numerical Comparison of Local Risk-Minimisation & Mean-Variance Hedging," Published Paper Series 2001-3, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    • Handle: RePEc:uts:ppaper:2001-3
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    Cited by:

    1. Xi Kleisinger-Yu & Vlatka Komaric & Martin Larsson & Markus Regez, 2019. "A multi-factor polynomial framework for long-term electricity forwards with delivery period," Papers 1908.08954, arXiv.org, revised Jun 2020.
    2. Ke Nian & Thomas F. Coleman & Yuying Li, 2018. "Learning minimum variance discrete hedging directly from the market," Quantitative Finance, Taylor & Francis Journals, vol. 18(7), pages 1115-1128, July.
    3. 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.
    4. David Heath & Eckhard Platen, 2002. "A variance reduction technique based on integral representations," Quantitative Finance, Taylor & Francis Journals, vol. 2(5), pages 362-369.
    5. 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.
    6. 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.
    7. Eckhard Platen, 2003. "Pricing and Hedging for Incomplete Jump Diffusion Benchmark Models," Research Paper Series 110, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Hélène Hamisultane, 2008. "Which Method for Pricing Weather Derivatives ?," Working Papers halshs-00355856, HAL.
    9. Dilip Madan, 2011. "Joint risk-neutral laws and hedging," IISE Transactions, Taylor & Francis Journals, vol. 43(12), pages 840-850.
    10. Akihiko Takahashi & Yukihiro Tsuzuki & Akira Yamazaki, 2011. "Hedging European Derivatives With The Polynomial Variance Swap Under Uncertain Volatility Environments," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(04), pages 485-505.
    11. Akihiko Takahashi & Yukihiro Tsuzuki & Akira Yamazaki, 2009. "Hedging European Derivatives with the Polynomial Variance Swap under Uncertain Volatility Environments," CIRJE F-Series CIRJE-F-653, CIRJE, Faculty of Economics, University of Tokyo.
    12. Schweizer, Martin, 1999. "A guided tour through quadratic hedging approaches," SFB 373 Discussion Papers 1999,96, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.

    More about this item

    Keywords

    incomplete markets; option pricing; hedging; local risk-minimization; mean-variance hedging; stochastic volatility; PDE and simulation methods;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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