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Variance Optimal Hedging for continuous time processes with independent increments and applications

Author

Listed:
  • St'ephane Goutte

    (LAGA, OPTEA)

  • Nadia Oudjane

    (LAGA)

  • Francesco Russo

    (LAGA, MathFi, CERMICS)

Abstract

For a large class of vanilla contingent claims, we establish an explicit F\"ollmer-Schweizer decomposition when the underlying is a process with independent increments (PII) and an exponential of a PII 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, 2009. "Variance Optimal Hedging for continuous time processes with independent increments and applications," Papers 0912.0372, arXiv.org.
  • Handle: RePEc:arx:papers:0912.0372
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    References listed on IDEAS

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    1. Huisman, Ronald & Mahieu, Ronald, 2003. "Regime jumps in electricity prices," Energy Economics, Elsevier, vol. 25(5), pages 425-434, September.
    2. 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.
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    4. Marco Frittelli, 2000. "The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 39-52, January.
    5. Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2008. "Analysis of Fourier transform valuation formulas and applications," Papers 0809.3405, arXiv.org, revised Sep 2009.
    6. Takuji Arai, 2005. "An extension of mean-variance hedging to the discontinuous case," Finance and Stochastics, Springer, vol. 9(1), pages 129-139, January.
    7. St'ephane Goutte & Nadia Oudjane & Francesco Russo, 2012. "Variance Optimal Hedging for discrete time processes with independent increments. Application to Electricity Markets," Papers 1205.4089, arXiv.org.
    8. Fred Espen Benth & Jan Kallsen & Thilo Meyer-Brandis, 2007. "A Non-Gaussian Ornstein-Uhlenbeck Process for Electricity Spot Price Modeling and Derivatives Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(2), pages 153-169.
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    Cited by:

    1. St'ephane Goutte & Nadia Oudjane & Francesco Russo, 2012. "Variance Optimal Hedging for discrete time processes with independent increments. Application to Electricity Markets," Papers 1205.4089, arXiv.org.
    2. René Aïd & Luciano Campi & Nicolas Langrené, 2010. "A structural risk-neutral model for pricing and hedging power derivatives," Working Papers hal-00525800, HAL.

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