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Variance optimal hedging for continuous time additive processes and applications

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  • 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.

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File URL: http://arxiv.org/pdf/1302.1965
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1302.1965.

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Date of creation: Feb 2013
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Handle: RePEc:arx:papers:1302.1965

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Web page: http://arxiv.org/

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References

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  1. 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, Finanza e Statistica.
  2. Thilo Meyer-Brandis & Peter Tankov, 2008. "Multi-Factor Jump-Diffusion Models Of Electricity Prices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(05), pages 503-528.
  3. Schwartz, Eduardo S, 1997. " The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-73, July.
  4. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
  5. 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.
  6. 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.
  7. 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.
  8. Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2010. "Analysis of Fourier Transform Valuation Formulas and Applications," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(3), pages 211-240.
  9. Takuji Arai, 2005. "An extension of mean-variance hedging to the discontinuous case," Finance and Stochastics, Springer, vol. 9(1), pages 129-139, January.
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Cited by:
  1. 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.
  2. Stephane Goutte & Armand Ngoupeyou, 2012. "Optimization problem and mean variance hedging on defaultable claims," Papers 1209.5953, arXiv.org.

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