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Approximate hedging with proportional transaction costs in stochastic volatility models with jumps

Author

Listed:
  • Huu Thai Nguyen

    (LMRS - Laboratoire de Mathématiques Raphaël Salem - UNIROUEN - Université de Rouen Normandie - NU - Normandie Université - CNRS - Centre National de la Recherche Scientifique)

  • Serguei Pergamenchtchikov

    (LMRS - Laboratoire de Mathématiques Raphaël Salem - UNIROUEN - Université de Rouen Normandie - NU - Normandie Université - CNRS - Centre National de la Recherche Scientifique)

Abstract

We extend the resutls for the problem of option replication under proportional transaction costs in \cite{Nguyen} to more general frameworks where stochastic volatility and jumps are combined to capture market's important features. In particular, we study the hedging error due to discrete readjustments by applying the Leland adjusting volatility principle to compensate transaction costs. In such contexts, jumps risk is approximately eliminated and the results established in \cite{Nguyen} are recovered.

Suggested Citation

  • Huu Thai Nguyen & Serguei Pergamenchtchikov, 2014. "Approximate hedging with proportional transaction costs in stochastic volatility models with jumps," Working Papers hal-00979199, HAL.
    • Handle: RePEc:hal:wpaper:hal-00979199
    Note: View the original document on HAL open archive server: https://hal.science/hal-00979199
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    References listed on IDEAS

    as
    1. Leland, Hayne E, 1985. "Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
    2. Yuri M. Kabanov & (*), Mher M. Safarian, 1997. "On Leland's strategy of option pricing with transactions costs," Finance and Stochastics, Springer, vol. 1(3), pages 239-250.
    3. Tankov, Peter & Voltchkova, Ekaterina, 2009. "Asymptotic analysis of hedging errors in models with jumps," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 2004-2027, June.
    4. Bjørn Eraker, 2004. "Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices," Journal of Finance, American Finance Association, vol. 59(3), pages 1367-1404, June.
    5. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    6. Huu Thai Nguyen & Serguei Pergamenchtchikov, 2012. "Approximate hedging problem with transaction costs in stochastic volatility markets," Working Papers hal-00747689, HAL.
    7. Peter Grandits & Werner Schachinger, 2001. "Leland's Approach to Option Pricing: The Evolution of a Discontinuity," Mathematical Finance, Wiley Blackwell, vol. 11(3), pages 347-355, July.
    8. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    9. Leif Andersen & Vladimir Piterbarg, 2007. "Moment explosions in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(1), pages 29-50, January.
    10. Mats Brod'en & Peter Tankov, 2010. "Tracking errors from discrete hedging in exponential L\'evy models," Papers 1003.0709, arXiv.org.
    11. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    12. repec:dau:papers:123456789/4055 is not listed on IDEAS
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    Keywords

    transaction costs. jump models; stochastic volatility; approximate hedging; theorem limit; super-hedging; quantile hedging;
    All these keywords.

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