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Stochastic Volatility: Risk Minimization and Model Risk


  • Christian-Olivier Ewald

    (School of Mathematics, University of Leeds)

  • Rolf Poulsen

    (Department of Mathematical Sciences, University of Copenhagen)

  • Klaus Reiner Schenk-Hoppe

    (School of Mathematics and Leeds University Business School, University of Leeds)


In this paper locally risk-minimizing hedge strategies for European-style contingent claims are derived and tested for a general class of stochastic volatility models. These strategies are as easy to implement as ordinary delta hedges, yet in realistic settings they produce markedly lower hedge errors. Our experimental investigations on model risk furthermore show that locally risk-minimizing hedges are robust with respect to parameter uncertainty as well as misspecifications of the stochastic volatility model.

Suggested Citation

  • Christian-Olivier Ewald & Rolf Poulsen & Klaus Reiner Schenk-Hoppe, 2007. "Stochastic Volatility: Risk Minimization and Model Risk," Swiss Finance Institute Research Paper Series 07-10, Swiss Finance Institute.
  • Handle: RePEc:chf:rpseri:rp0710

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    References listed on IDEAS

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    3. Peter Bank & Dietmar Baum, 2004. "Hedging and Portfolio Optimization in Financial Markets with a Large Trader," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 1-18.
    4. Lux, Thomas, 1997. "Time variation of second moments from a noise trader/infection model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(1), pages 1-38, November.
    5. Brock, W.A. & Hommes, C.H. & Wagener, F.O.O., 2009. "More hedging instruments may destabilize markets," Journal of Economic Dynamics and Control, Elsevier, vol. 33(11), pages 1912-1928, November.
    6. Alfarano, Simone & Lux, Thomas & Wagner, Friedrich, 2008. "Time variation of higher moments in a financial market with heterogeneous agents: An analytical approach," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 101-136, January.
    7. Chiarella, Carl & Dieci, Roberto & Gardini, Laura, 2006. "Asset price and wealth dynamics in a financial market with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1755-1786.
    8. Evstigneev, Igor V. & Hens, Thorsten & Schenk-Hoppé, Klaus Reiner, 2008. "Globally evolutionarily stable portfolio rules," Journal of Economic Theory, Elsevier, vol. 140(1), pages 197-228, May.
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    10. Igor Evstigneev & Thorsten Hens & Klaus Schenk-Hoppé, 2006. "Evolutionary stable stock markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(2), pages 449-468, January.
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    12. Igor V. Evstigneev & Thorsten Hens & Klaus Reiner Schenk-Hoppé, 2011. "Survival and Evolutionary Stability of the Kelly Rule," World Scientific Book Chapters,in: THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 20, pages 273-284 World Scientific Publishing Co. Pte. Ltd..
    13. Igor V. Evstigneev & Thorsten Hens & Klaus Reiner Schenk-Hoppé, 2008. "Evolutionary Finance," Swiss Finance Institute Research Paper Series 08-14, Swiss Finance Institute.
    14. Carl Chiarella & Xue-Zhong He & Min Zheng, 2007. "The Stochastic Dynamics of Speculative Prices," Research Paper Series 208, Quantitative Finance Research Centre, University of Technology, Sydney.
    15. Zeeman, E. C., 1974. "On the unstable behaviour of stock exchanges," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 39-49, March.
    16. Palczewski, Jan & Schenk-Hoppé, Klaus Reiner, 2010. "Market selection of constant proportions investment strategies in continuous time," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 248-266, March.
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    More about this item


    Locally risk-minimizing hedge; delta hedge; stochastic volatility; model risk;

    JEL classification:

    • C90 - Mathematical and Quantitative Methods - - Design of Experiments - - - General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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