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Risk minimization in stochastic volatility models: model risk and empirical performance

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  • Rolf Poulsen
  • Klaus Reiner Schenk-Hoppe
  • Christian-Oliver Ewald

Abstract

In this paper the performance of locally risk-minimizing delta hedge strategies for European options in stochastic volatility models is studied from an experimental as well as from an empirical perspective. These hedge strategies are derived for a large class of diffusion-type stochastic volatility models, and they are as easy to implement as usual delta hedges. Our simulation results on model risk show that these risk-minimizing hedges are robust with respect to uncertainty and misconceptions about the underlying data generating process. The empirical study, which includes the US sub-prime crisis period, documents that in equity markets risk-minimizing delta hedges consistently outperform usual delta hedges by approximately halving the standard deviation of the profit-and-loss ratio.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:quantf:v:9:y:2009:i:6:p:693-704
    DOI: 10.1080/14697680902852738
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    References listed on IDEAS

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    Cited by:

    1. 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.
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    3. Chuang, Wen-I & Huang, Teng-Ching & Lin, Bing-Huei, 2013. "Predicting volatility using the Markov-switching multifractal model: Evidence from S&P 100 index and equity options," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 168-187.
    4. Leonidas S. Rompolis & Elias Tzavalis, 2017. "Pricing and hedging contingent claims using variance and higher order moment swaps," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 531-550, April.
    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. 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.
    7. Dirk Becherer & Klebert Kentia, 2017. "Hedging under generalized good-deal bounds and model uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(1), pages 171-214, August.
    8. Ewald, Christian-Oliver & Nawar, Roy & Siu, Tak Kuen, 2013. "Minimal variance hedging of natural gas derivatives in exponential Lévy models: Theory and empirical performance," Energy Economics, Elsevier, vol. 36(C), pages 97-107.
    9. Mozumder, Sharif & Dempsey, Michael & Kabir, M. Humayun & Choudhry, Taufiq, 2016. "An improved framework for approximating option prices with application to option portfolio hedging," Economic Modelling, Elsevier, vol. 59(C), pages 285-296.
    10. Srikanth Iyer & Seema Nanda & Swapnil Kumar, 2013. "An Empirical Comparison of Two Stochastic Volatility Models using Indian Market Data," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 20(3), pages 243-259, September.
    11. Yunbi An & Wulin Suo, 2009. "An Empirical Comparison of Option‐Pricing Models in Hedging Exotic Options," Financial Management, Financial Management Association International, vol. 38(4), pages 889-914, December.
    12. Hull, John & White, Alan, 2017. "Optimal delta hedging for options," Journal of Banking & Finance, Elsevier, vol. 82(C), pages 180-190.
    13. Ceci, Claudia & Colaneri, Katia & Cretarola, Alessandra, 2017. "Unit-linked life insurance policies: Optimal hedging in partially observable market models," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 149-163.
    14. Coqueret, Guillaume & Tavin, Bertrand, 2016. "An investigation of model risk in a market with jumps and stochastic volatility," European Journal of Operational Research, Elsevier, vol. 253(3), pages 648-658.
    15. Martin Tegnér & Rolf Poulsen, 2018. "Volatility Is Log-Normal—But Not for the Reason You Think," Risks, MDPI, Open Access Journal, vol. 6(2), pages 1-16, April.
    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. Sai Hung Marten Ting & Christian-Oliver Ewald, 2013. "On the performance of asymptotic locally risk minimising hedges in the Heston stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 939-954, May.
    18. Laurini Márcio Poletti, 2013. "A Hybrid Data Cloning Maximum Likelihood Estimator for Stochastic Volatility Models," Journal of Time Series Econometrics, De Gruyter, vol. 5(2), pages 193-229, May.
    19. Yao Tung Huang & Yue Kuen Kwok, 2016. "Regression-based Monte Carlo methods for stochastic control models: variable annuities with lifelong guarantees," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 905-928, June.
    20. Carol Alexander & Andreas Kaeck, 2012. "Does model fit matter for hedging? Evidence from FTSE 100 options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 32(7), pages 609-638, July.
    21. Kang, Boda & Ziveyi, Jonathan, 2018. "Optimal surrender of guaranteed minimum maturity benefits under stochastic volatility and interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 43-56.
    22. Carol Alexander & Alexander Rubinov & Markus Kalepky & Stamatis Leontsinis, 2012. "Regime‐dependent smile‐adjusted delta hedging," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 32(3), pages 203-229, March.
    23. Anatoliy Swishchuk, 2013. "Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8660, February.
    24. Simon Ellersgaard & Martin Jönsson & Rolf Poulsen, 2017. "The Fundamental Theorem of Derivative Trading - exposition, extensions and experiments," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 515-529, April.
    25. Dirk Becherer & Klebert Kentia, 2016. "Hedging under generalized good-deal bounds and model uncertainty," Papers 1607.04488, arXiv.org, revised Apr 2017.

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