IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1506.03898.html
   My bibliography  Save this paper

Numerical analysis on local risk-minimization forexponential L\'evy models

Author

Listed:
  • Takuji Arai
  • Yuto Imai
  • Ryoichi Suzuki

Abstract

We illustrate how to compute local risk minimization (LRM) of call options for exponential L\'evy models. We have previously obtained a representation of LRM for call options; here we transform it into a form that allows use of the fast Fourier transform method suggested by Carr & Madan. In particular, we consider Merton jump-diffusion models and variance gamma models as concrete applications.

Suggested Citation

  • Takuji Arai & Yuto Imai & Ryoichi Suzuki, 2015. "Numerical analysis on local risk-minimization forexponential L\'evy models," Papers 1506.03898, arXiv.org.
    • Handle: RePEc:arx:papers:1506.03898
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1506.03898
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. P. Leoni & N. Vandaele & M. Vanmaele, 2014. "Hedging strategies for energy derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 14(10), pages 1725-1737, October.
    2. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    3. Kiseop Lee & Seongjoo Song, 2007. "Insiders' hedging in a jump diffusion model," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 537-545.
    4. Jose Scheinkman & René Carmona & Erhan Cinlare & Ivar Ekeland & Elyès Jouini & Nizar Touzi, 2010. "Paris-Princeton Lectures on Mathematical Finance," Post-Print halshs-00706281, HAL.
    5. Ewald, Christian-Oliver & Nawar, Roy & Siu, Tak Kuen, 2013. "Minimal variance hedging of natural gas derivatives in exponential Lévy models: Theory and empirical performance," Energy Economics, Elsevier, vol. 36(C), pages 97-107.
    6. Jouini,E. & Cvitanic,J. & Musiela,Marek (ed.), 2001. "Handbooks in Mathematical Finance," Cambridge Books, Cambridge University Press, number 9780521792370.
    7. Abdou Kélani & François Quittard-Pinon, 2014. "Pricing, Hedging and Assessing Risk in a General Lévy Context," Bankers, Markets & Investors, ESKA Publishing, issue 131, pages 30-42, July-Augu.
    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. Takuji Arai & Yuto Imai, 2016. "On the difference between locally risk-minimizing and delta hedging strategies for exponential L\'evy models," Papers 1610.09085, arXiv.org.

    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. Takuji Arai & Yuto Imai & Ryoichi Suzuki, 2016. "Numerical Analysis On Local Risk-Minimization For Exponential Lévy Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-27, March.
    2. Wei Wang & Linyi Qian & Wensheng Wang, 2016. "Hedging of contingent claims written on non traded assets under Markov-modulated models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(12), pages 3577-3595, June.
    3. Ewald, Christian-Oliver & Nawar, Roy & Siu, Tak Kuen, 2013. "Minimal variance hedging of natural gas derivatives in exponential Lévy models: Theory and empirical performance," Energy Economics, Elsevier, vol. 36(C), pages 97-107.
    4. Silva, Felipe Bastos Gurgel, 2021. "Fiscal Deficits, Bank Credit Risk, and Loan-Loss Provisions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 56(5), pages 1537-1589, August.
    5. Alev{s} v{C}ern'y & Stephan Denkl & Jan Kallsen, 2013. "Hedging in L\'evy Models and the Time Step Equivalent of Jumps," Papers 1309.7833, arXiv.org, revised Jul 2017.
    6. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    7. Carol Alexandra & Leonardo M. Nogueira, 2005. "Optimal Hedging and Scale Inavriance: A Taxonomy of Option Pricing Models," ICMA Centre Discussion Papers in Finance icma-dp2005-10, Henley Business School, University of Reading, revised Nov 2005.
    8. Christophe Chorro & Florian Ielpo & Benoît Sévi, 2017. "The contribution of jumps to forecasting the density of returns," Post-Print halshs-01442618, HAL.
    9. Peter Carr & Liuren Wu, 2014. "Static Hedging of Standard Options," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 3-46.
    10. Kathrin Glau & Ricardo Pachon & Christian Potz, 2019. "Speed-up credit exposure calculations for pricing and risk management," Papers 1912.01280, arXiv.org.
    11. Pringles, Rolando & Olsina, Fernando & Penizzotto, Franco, 2020. "Valuation of defer and relocation options in photovoltaic generation investments by a stochastic simulation-based method," Renewable Energy, Elsevier, vol. 151(C), pages 846-864.
    12. Sandrine Lardic & Claire Gauthier, 2003. "Un modèle multifactoriel des spreads de crédit : estimation sur panels complets et incomplets," Économie et Prévision, Programme National Persée, vol. 159(3), pages 53-69.
    13. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    14. Sang Byung Seo & Jessica A. Wachter, 2019. "Option Prices in a Model with Stochastic Disaster Risk," Management Science, INFORMS, vol. 65(8), pages 3449-3469, August.
    15. John Driffill & Turalay Kenc & Martin Sola, 2013. "Real Options With Priced Regime-Switching Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(05), pages 1-30.
    16. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, January.
    17. Prakash Chakraborty & Kiseop Lee, 2022. "Bond Prices Under Information Asymmetry and a Short Rate with Instantaneous Feedback," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 613-634, June.
    18. Carvalho, Augusto & Guimaraes, Bernardo, 2018. "State-controlled companies and political risk: Evidence from the 2014 Brazilian election," Journal of Public Economics, Elsevier, vol. 159(C), pages 66-78.
    19. Jurczenko, Emmanuel & Maillet, Bertrand & Negrea, Bogdan, 2002. "Revisited multi-moment approximate option pricing models: a general comparison (Part 1)," LSE Research Online Documents on Economics 24950, London School of Economics and Political Science, LSE Library.
    20. Viktor Stojkoski & Trifce Sandev & Lasko Basnarkov & Ljupco Kocarev & Ralf Metzler, 2020. "Generalised geometric Brownian motion: Theory and applications to option pricing," Papers 2011.00312, arXiv.org.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:1506.03898. See general information about how to correct material in RePEc.

    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 bibliographic 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.

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

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.