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Variance Optimal Hedging for discrete time processes with independent increments. Application to Electricity Markets

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Listed:
  • St'ephane Goutte

    (LAGA)

  • Nadia Oudjane

    (LAGA)

  • Francesco Russo

    (CERMICS, INRIA Rocquencourt, UMA)

Abstract

We consider the discretized version of a (continuous-time) two-factor model introduced by Benth and coauthors for the electricity markets. For this model, the underlying is the exponent of a sum of independent random variables. We provide and test an algorithm, which is based on the celebrated Foellmer-Schweizer decomposition for solving the mean-variance hedging problem. In particular, we establish that decomposition explicitely, for a large class of vanilla contingent claims. Interest is devoted in the choice of rebalancing dates and its impact on the hedging error, regarding the payoff regularity and the non stationarity of the log-price process.

Suggested Citation

  • 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.
  • Handle: RePEc:arx:papers:1205.4089
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    References listed on IDEAS

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    1. Föllmer, H. & Schweizer, M., 1989. "Hedging by Sequential Regression: an Introduction to the Mathematics of Option Trading," ASTIN Bulletin, Cambridge University Press, vol. 19(S1), pages 29-42, November.
    2. Flavio Angelini & Stefano Herzel, 2007. "Measuring the error of dynamic hedging: a Laplace transform approach," Quaderni del Dipartimento di Economia, Finanza e Statistica 33/2007, Università di Perugia, Dipartimento Economia.
    3. Flavio Angelini & Stefano Herzel, 2010. "Explicit formulas for the minimal variance hedging strategy in a martingale case," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 33(1), pages 63-79, May.
    4. Aleš Černý, 2007. "Optimal Continuous‐Time Hedging With Leptokurtic Returns," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 175-203, April.
    5. Ales Cerny, 2004. "Dynamic programming and mean-variance hedging in discrete time," Applied Mathematical Finance, Taylor & Francis Journals, vol. 11(1), pages 1-25.
    6. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    7. 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.
    8. 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.
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    Cited by:

    1. 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.
    2. St'ephane Goutte & Nadia Oudjane & Francesco Russo, 2013. "Variance optimal hedging for continuous time additive processes and applications," Papers 1302.1965, arXiv.org.
    3. 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.
    4. 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.
    5. 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.
    6. Fred Benth & Nils Detering, 2015. "Pricing and hedging Asian-style options on energy," Finance and Stochastics, Springer, vol. 19(4), pages 849-889, October.
    7. Debbie Dupuis, Geneviève Gauthier, and Fréderic Godin, 2016. "Short-term Hedging for an Electricity Retailer," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2).

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