IDEAS home Printed from https://ideas.repec.org/p/arx/papers/math-0610219.html
   My bibliography  Save this paper

The minimal entropy martingale measure for general Barndorff-Nielsen/Shephard models

Author

Listed:
  • Thorsten Rheinlander
  • Gallus Steiger

Abstract

We determine the minimal entropy martingale measure for a general class of stochastic volatility models where both price process and volatility process contain jump terms which are correlated. This generalizes previous studies which have treated either the geometric L\'{e}vy case or continuous price processes with an orthogonal volatility process. We proceed by linking the entropy measure to a certain semi-linear integro-PDE for which we prove the existence of a classical solution.

Suggested Citation

  • Thorsten Rheinlander & Gallus Steiger, 2006. "The minimal entropy martingale measure for general Barndorff-Nielsen/Shephard models," Papers math/0610219, arXiv.org.
    • Handle: RePEc:arx:papers:math/0610219
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/math/0610219
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Elisa Nicolato & Emmanouil Venardos, 2003. "Option Pricing in Stochastic Volatility Models of the Ornstein‐Uhlenbeck type," Mathematical Finance, Wiley Blackwell, vol. 13(4), pages 445-466, October.
    2. Fabio Bellini & Marco Frittelli, 2002. "On the Existence of Minimax Martingale Measures," Mathematical Finance, Wiley Blackwell, vol. 12(1), pages 1-21, January.
    3. Tahir Choulli & Christophe Stricker, 2005. "Minimal Entropy–Hellinger Martingale Measure In Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 15(3), pages 465-490, July.
    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. Jan Kallsen & Johannes Muhle-Karbe, 2009. "Utility maximization in models with conditionally independent increments," Papers 0911.3608, arXiv.org.
    2. Thorsten Rheinländer & Jenny Sexton, 2011. "Hedging Derivatives," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8062, December.
    3. Hubalek, Friedrich & Sgarra, Carlo, 2009. "On the Esscher transforms and other equivalent martingale measures for Barndorff-Nielsen and Shephard stochastic volatility models with jumps," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2137-2157, July.
    4. Friedrich Hubalek & Petra Posedel, 2008. "Asymptotic analysis for a simple explicit estimator in Barndorff-Nielsen and Shephard stochastic volatility models," Papers 0807.3479, arXiv.org.
    5. Markus Hess, 2019. "Optimal Equivalent Probability Measures under Enlarged Filtrations," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 813-839, December.
    6. Choulli, Tahir & Vandaele, Nele & Vanmaele, Michèle, 2010. "The Föllmer-Schweizer decomposition: Comparison and description," Stochastic Processes and their Applications, Elsevier, vol. 120(6), pages 853-872, June.

    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. Hubalek, Friedrich & Sgarra, Carlo, 2009. "On the Esscher transforms and other equivalent martingale measures for Barndorff-Nielsen and Shephard stochastic volatility models with jumps," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2137-2157, July.
    2. Friedrich Hubalek & Carlo Sgarra, 2008. "On the Esscher transforms and other equivalent martingale measures for Barndorff-Nielsen and Shephard stochastic volatility models with jumps," Papers 0807.1227, arXiv.org.
    3. Rheinlander, Thorsten & Steiger, Gallus, 2006. "The minimal entropy martingale measure for general Barndorff-Nielsen/Shephard models," LSE Research Online Documents on Economics 16351, London School of Economics and Political Science, LSE Library.
    4. Choulli, Tahir & Stricker, Christophe, 2009. "Comparing the minimal Hellinger martingale measure of order q to the q-optimal martingale measure," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1368-1385, April.
    5. Almut Veraart & Luitgard Veraart, 2012. "Stochastic volatility and stochastic leverage," Annals of Finance, Springer, vol. 8(2), pages 205-233, May.
    6. Martin Keller-Ressel & Antonis Papapantoleon & Josef Teichmann, 2009. "The affine LIBOR models," Papers 0904.0555, arXiv.org, revised Jul 2011.
    7. Robert Stelzer & Jovana Zaviv{s}in, 2014. "Derivative pricing under the possibility of long memory in the supOU stochastic volatility model," Papers 1404.1773, arXiv.org.
    8. Kostrova, Alisa & Britz, Wolfgang & Finger, Robert & Djanibekov, Utkur, 2016. "Real Options Approach And Stochastic Programming In Farm Level Analysis: The Case Of Short-Rotation Coppice Cultivation," 56th Annual Conference, Bonn, Germany, September 28-30, 2016 244864, German Association of Agricultural Economists (GEWISOLA).
    9. Badics, Tamás, 2011. "Az arbitrázs preferenciákkal történő karakterizációjáról [On the characterization of arbitrage in terms of preferences]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(9), pages 727-742.
    10. Laurent, Sébastien & Shi, Shuping, 2020. "Volatility estimation and jump detection for drift–diffusion processes," Journal of Econometrics, Elsevier, vol. 217(2), pages 259-290.
    11. Fred Espen Benth & Martin Groth & Rodwell Kufakunesu, 2007. "Valuing Volatility and Variance Swaps for a Non-Gaussian Ornstein-Uhlenbeck Stochastic Volatility Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(4), pages 347-363.
    12. Takuji Arai & Yuto Imai, 2024. "Option pricing for Barndorff-Nielsen and Shephard model by supervised deep learning," Papers 2402.00445, arXiv.org.
    13. Michael Roberts & Indranil SenGupta, 2020. "Sequential hypothesis testing in machine learning, and crude oil price jump size detection," Papers 2004.08889, arXiv.org, revised Dec 2020.
    14. Michael Mania & Revaz Tevzadze, 2016. "On regularity of primal and dual dynamic value functions related to investment problem," Papers 1604.00525, arXiv.org.
    15. Acciaio Beatrice, 2005. "Absolutely continuous optimal martingale measures," Statistics & Risk Modeling, De Gruyter, vol. 23(2), pages 81-100, February.
    16. Griffin, J.E. & Steel, M.F.J., 2010. "Bayesian inference with stochastic volatility models using continuous superpositions of non-Gaussian Ornstein-Uhlenbeck processes," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2594-2608, November.
    17. Abel Rodriguez & Enrique ter Horst, 2008. "Measuring expectations in options markets: An application to the SP500 index," Papers 0901.0033, arXiv.org.
    18. Piotr Szczepocki, 2020. "Application of iterated filtering to stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck process," Statistics in Transition New Series, Polish Statistical Association, vol. 21(2), pages 173-187, June.
    19. Klöppel Susanne & Schweizer Martin, 2007. "Dynamic utility-based good deal bounds," Statistics & Risk Modeling, De Gruyter, vol. 25(4), pages 285-309, October.

    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:math/0610219. 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.