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Variance optimal hedging for continuous time additive processes and applications

Author

Listed:
  • St'ephane Goutte

    (LAGA)

  • Nadia Oudjane

    (FiME Lab)

  • Francesco Russo

    (UMA)

Abstract

For a large class of vanilla contingent claims, we establish an explicit F\"ollmer-Schweizer decomposition when the underlying is an exponential of an additive process. This allows to provide an efficient algorithm for solving the mean variance hedging problem. Applications to models derived from the electricity market are performed.

Suggested Citation

  • St'ephane Goutte & Nadia Oudjane & Francesco Russo, 2013. "Variance optimal hedging for continuous time additive processes and applications," Papers 1302.1965, arXiv.org.
    • Handle: RePEc:arx:papers:1302.1965
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    References listed on IDEAS

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    10. repec:dau:papers:123456789/11532 is not listed on IDEAS
    11. Arai, Takuji, 2005. "Some properties of the variance-optimal martingale measure for discontinuous semimartingales," Statistics & Probability Letters, Elsevier, vol. 74(2), pages 163-170, September.
    12. Fred Espen Benth & Giulia Di Nunno & Arne Løkka & Bernt Øksendal & Frank Proske, 2003. "Explicit Representation of the Minimal Variance Portfolio in Markets Driven by Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 55-72, January.
    13. Stephan Denkl & Martina Goy & Jan Kallsen & Johannes Muhle-Karbe & Arnd Pauwels, 2009. "On the Performance of Delta Hedging Strategies in Exponential L\'evy Models," Papers 0911.4859, arXiv.org, revised May 2011.
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    Citations

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    Cited by:

    1. Julien Chevallier & Stéphane Goutte, 2014. "The goodness-of-fit of the fuel-switching price using the mean-reverting Lévy jump process," Working Papers 2014-285, Department of Research, Ipag Business School.
    2. Boroumand, Raphaël Homayoun & Goutte, Stéphane & Porcher, Simon & Porcher, Thomas, 2015. "Hedging strategies in energy markets: The case of electricity retailers," Energy Economics, Elsevier, vol. 51(C), pages 503-509.
    3. Takuji Arai & Yuto Imai, 2017. "A closed-form representation of mean-variance hedging for additive processes via Malliavin calculus," Papers 1702.07556, arXiv.org, revised Nov 2017.
    4. Tegnér, Martin & Ernstsen, Rune Ramsdal & Skajaa, Anders & Poulsen, Rolf, 2017. "Risk-minimisation in electricity markets: Fixed price, unknown consumption," Energy Economics, Elsevier, vol. 68(C), pages 423-439.
    5. Julien Chevallier & Stéphane Goutte, 2017. "Estimation of Lévy-driven Ornstein–Uhlenbeck processes: application to modeling of $$\hbox {CO}_2$$ CO 2 and fuel-switching," Annals of Operations Research, Springer, vol. 255(1), pages 169-197, August.
    6. Stephane Goutte & Armand Ngoupeyou, 2012. "Optimization problem and mean variance hedging on defaultable claims," Papers 1209.5953, arXiv.org.
    7. Ismail Laachir & Francesco Russo, 2016. "BSDEs, càdlàg martingale problems and orthogonalisation under basis risk," Working Papers hal-01086227, HAL.
    8. Goutte, Stéphane & Ngoupeyou, Armand, 2015. "The use of BSDEs to characterize the mean–variance hedging problem and the variance optimal martingale measure for defaultable claims," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1323-1351.
    9. Terry Lyons & Sina Nejad & Imanol Perez Arribas, 2019. "Nonparametric pricing and hedging of exotic derivatives," Papers 1905.00711, arXiv.org.
    10. Carmine De Franco & Peter Tankov & Xavier Warin, 2012. "Numerical methods for the quadratic hedging problem in Markov models with jumps," Papers 1206.5393, arXiv.org, revised Dec 2013.
    11. Fred Benth & Nils Detering, 2015. "Pricing and hedging Asian-style options on energy," Finance and Stochastics, Springer, vol. 19(4), pages 849-889, October.

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