IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1302.1965.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1302.1965
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    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.
    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 923-973, July.
    4. Takuji Arai, 2005. "An extension of mean-variance hedging to the discontinuous case," Finance and Stochastics, Springer, vol. 9(1), pages 129-139, January.
    5. 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.
    6. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
    7. 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.
    8. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    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. Stephane Goutte & Armand Ngoupeyou, 2012. "Optimization problem and mean variance hedging on defaultable claims," Papers 1209.5953, arXiv.org.
    5. Ismail Laachir & Francesco Russo, 2016. "BSDEs, càdlàg martingale problems and orthogonalisation under basis risk," Working Papers hal-01086227, HAL.
    6. 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.
    7. 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.
    8. Terry Lyons & Sina Nejad & Imanol Perez Arribas, 2019. "Nonparametric pricing and hedging of exotic derivatives," Papers 1905.00711, arXiv.org.
    9. 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.
    10. Fred Benth & Nils Detering, 2015. "Pricing and hedging Asian-style options on energy," Finance and Stochastics, Springer, vol. 19(4), pages 849-889, October.
    11. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. 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.
    3. 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.
    4. Hervé-Mignucci, Morgan, 2011. "Rôle du signal prix du carbone sur les décisions d'investissement des entreprises," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/8200 edited by Keppler, Jan Horst, October.
    5. Weijermars, R. & Sun, Z., 2018. "Regression analysis of historic oil prices: A basis for future mean reversion price scenarios," Global Finance Journal, Elsevier, vol. 35(C), pages 177-201.
    6. 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.
    7. Aouam, Tarik & Muthuraman, Kumar & Rardin, Ronal L., 2016. "Robust optimization policy benchmarks and modeling errors in natural gas," European Journal of Operational Research, Elsevier, vol. 250(3), pages 807-815.
    8. Robert Jarrow, 2010. "Convenience yields," Review of Derivatives Research, Springer, vol. 13(1), pages 25-43, April.
    9. Melnikov, Alexander & Romaniuk, Yulia, 2006. "Evaluating the performance of Gompertz, Makeham and Lee-Carter mortality models for risk management with unit-linked contracts," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 310-329, December.
    10. Peter Lindberg, 2012. "Optimal partial hedging of an American option: shifting the focus to the expiration date," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(3), pages 221-243, June.
    11. Unterschultz, James R., 2000. "New Instruments For Co-Ordination And Risk Sharing Within The Canadian Beef Industry," Project Report Series 24046, University of Alberta, Department of Resource Economics and Environmental Sociology.
    12. repec:dau:papers:123456789/13631 is not listed on IDEAS
    13. Chiarella, Carl & Kang, Boda & Nikitopoulos, Christina Sklibosios & Tô, Thuy-Duong, 2013. "Humps in the volatility structure of the crude oil futures market: New evidence," Energy Economics, Elsevier, vol. 40(C), pages 989-1000.
    14. Han, Liyan & Xu, Yang & Yin, Libo, 2017. "Does investor attention matter? The attention-return relation in gold futures market," Economics Discussion Papers 2017-37, Kiel Institute for the World Economy (IfW).
    15. Chuong Luong & Nikolai Dokuchaev, 2016. "Modeling Dependency Of Volatility On Sampling Frequency Via Delay Equations," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 1-21, June.
    16. Bulan, Laarni & Mayer, Christopher & Somerville, C. Tsuriel, 2009. "Irreversible investment, real options, and competition: Evidence from real estate development," Journal of Urban Economics, Elsevier, vol. 65(3), pages 237-251, May.
    17. Asai, Manabu & McAleer, Michael, 2015. "Leverage and feedback effects on multifactor Wishart stochastic volatility for option pricing," Journal of Econometrics, Elsevier, vol. 187(2), pages 436-446.
    18. Noufel Frikha & Vincent Lemaire, 2012. "Joint Modelling of Gas and Electricity spot prices," Post-Print hal-00421289, HAL.
    19. Hamidi, Benjamin & Maillet, Bertrand & Prigent, Jean-Luc, 2014. "A dynamic autoregressive expectile for time-invariant portfolio protection strategies," Journal of Economic Dynamics and Control, Elsevier, vol. 46(C), pages 1-29.
    20. Brix, Anne Floor & Lunde, Asger & Wei, Wei, 2018. "A generalized Schwartz model for energy spot prices — Estimation using a particle MCMC method," Energy Economics, Elsevier, vol. 72(C), pages 560-582.
    21. Jonathan M. Godbey & Jimmy E. Hilliard, 2007. "Adjusting stacked-hedge ratios for stochastic convenience yield: a minimum variance approach," Quantitative Finance, Taylor & Francis Journals, vol. 7(3), pages 289-300.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1302.1965. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators). General contact details of provider: http://arxiv.org/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.