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

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  • 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.

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File URL: http://arxiv.org/pdf/1205.4089
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Paper provided by arXiv.org in its series Papers with number 1205.4089.

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Date of creation: May 2012
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Handle: RePEc:arx:papers:1205.4089

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Web page: http://arxiv.org/

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  1. Ales Čern�, 2007. "Optimal Continuous-Time Hedging With Leptokurtic Returns," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 17(2), pages 175-203.
  2. Flavio Angelini & Stefano Herzel, 2007. "Measuring the error of dynamic hedging: a Laplace transform approach," Quaderni del Dipartimento di Economia, Finanza e Statistica, Università di Perugia, Dipartimento Economia, Finanza e Statistica 33/2007, Università di Perugia, Dipartimento Economia, Finanza e Statistica.
  3. Flavio Angelini & Stefano Herzel, 2007. "Explicit formulas for the minimal variance hedging strategy in a martingale case," Quaderni del Dipartimento di Economia, Finanza e Statistica, Università di Perugia, Dipartimento Economia, Finanza e Statistica 35/2007, Università di Perugia, Dipartimento Economia, Finanza e Statistica.
  4. 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, Taylor & Francis Journals, vol. 14(2), pages 153-169.
  5. 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.
  6. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, Elsevier, vol. 7(3), pages 229-263, September.
  7. Ales Cerny, 2004. "Dynamic programming and mean-variance hedging in discrete time," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 11(1), pages 1-25.
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Cited by:
  1. 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.
  2. St\'ephane Goutte & Nadia Oudjane & Francesco Russo, 2013. "Variance optimal hedging for continuous time additive processes and applications," Papers 1302.1965, arXiv.org.

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