IDEAS home Printed from https://ideas.repec.org/a/spr/decfin/v37y2014i2p319-327.html
   My bibliography  Save this article

Symmetry and Bates’ rule in Ornstein–Uhlenbeck stochastic volatility models

Author

Listed:
  • José Fajardo

Abstract

We find necessary and sufficient conditions for the market symmetry property, introduced by Fajardo and Mordecki (Quant Finance 6(3):219–227, 2006 ), to hold in the Ornstein–Uhlenbeck stochastic volatility model, henceforth OU–SV. In particular, we address the non-Gaussian OU–SV model proposed by Barndorff-Nielsen and Shephard (J R Stat Soc B 63(Part 2):167–241, 2001 ). Also, we prove the Bates’ rule for these models. Copyright Springer-Verlag 2014

Suggested Citation

  • José Fajardo, 2014. "Symmetry and Bates’ rule in Ornstein–Uhlenbeck stochastic volatility models," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 319-327, October.
    • Handle: RePEc:spr:decfin:v:37:y:2014:i:2:p:319-327
    DOI: 10.1007/s10203-012-0136-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10203-012-0136-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10203-012-0136-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Albert N. Shiryaev & Jan Kallsen, 2002. "The cumulant process and Esscher's change of measure," Finance and Stochastics, Springer, vol. 6(4), pages 397-428.
    2. Ernst Eberlein & Antonis Papapantoleon & Albert Shiryaev, 2008. "On the duality principle in option pricing: semimartingale setting," Finance and Stochastics, Springer, vol. 12(2), pages 265-292, April.
    3. Jos� Fajardo & Ernesto Mordecki, 2014. "Skewness premium with L�vy processes," Quantitative Finance, Taylor & Francis Journals, vol. 14(9), pages 1619-1626, September.
    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    5. 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.
    6. JosE Fajardo & Ernesto Mordecki, 2006. "Symmetry and duality in Levy markets," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 219-227.
    7. Bates, David S., 1996. "Dollar jump fears, 1984-1992: distributional abnormalities implicit in currency futures options," Journal of International Money and Finance, Elsevier, vol. 15(1), pages 65-93, February.
    8. Bates, David S, 1991. "The Crash of '87: Was It Expected? The Evidence from Options Markets," Journal of Finance, American Finance Association, vol. 46(3), pages 1009-1044, July.
    9. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    10. Friedrich Hubalek & Petra Posedel, 2011. "Joint analysis and estimation of stock prices and trading volume in Barndorff-Nielsen and Shephard stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 11(6), pages 917-932.
    11. Fajardo, José & Mordecki, Ernesto, 2010. "Market symmetry in time-changed Brownian models," Finance Research Letters, Elsevier, vol. 7(1), pages 53-59, March.
    12. Michael Schmutz, 2011. "Semi-static hedging for certain Margrabe-type options with barriers," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 979-986.
    13. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    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. Fajardo, José, 2015. "Barrier style contracts under Lévy processes: An alternative approach," Journal of Banking & Finance, Elsevier, vol. 53(C), pages 179-187.

    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. Jondeau, Eric & Rockinger, Michael, 2000. "Reading the smile: the message conveyed by methods which infer risk neutral densities," Journal of International Money and Finance, Elsevier, vol. 19(6), pages 885-915, December.
    2. José Fajardo & Ernesto Mordecki, 2006. "Skewness Premium with Lévy Processes," IBMEC RJ Economics Discussion Papers 2006-04, Economics Research Group, IBMEC Business School - Rio de Janeiro.
    3. 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.
    4. 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.
    5. Malz, Allan M., 1996. "Using option prices to estimate realignment probabilities in the European Monetary System: the case of sterling-mark," Journal of International Money and Finance, Elsevier, vol. 15(5), pages 717-748, October.
    6. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.
    7. Björn Lutz, 2010. "Pricing of Derivatives on Mean-Reverting Assets," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-02909-7, December.
    8. Ako Doffou & Jimmy E. Hilliard, 2001. "Pricing Currency Options Under Stochastic Interest Rates And Jump-Diffusion Processes," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 24(4), pages 565-585, December.
    9. Cheng Few Lee & Yibing Chen & John Lee, 2020. "Alternative Methods to Derive Option Pricing Models: Review and Comparison," World Scientific Book Chapters, in: Cheng Few Lee & John C Lee (ed.), HANDBOOK OF FINANCIAL ECONOMETRICS, MATHEMATICS, STATISTICS, AND MACHINE LEARNING, chapter 102, pages 3573-3617, World Scientific Publishing Co. Pte. Ltd..
    10. Rombouts, Jeroen V.K. & Stentoft, Lars, 2015. "Option pricing with asymmetric heteroskedastic normal mixture models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 635-650.
    11. David S. Bates, 1995. "Testing Option Pricing Models," NBER Working Papers 5129, National Bureau of Economic Research, Inc.
    12. Chen, An-Sing & Leung, Mark T., 2005. "Modeling time series information into option prices: An empirical evaluation of statistical projection and GARCH option pricing model," Journal of Banking & Finance, Elsevier, vol. 29(12), pages 2947-2969, December.
    13. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 2000. "Pricing and hedging long-term options," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 277-318.
    14. Bin Xie & Weiping Li & Nan Liang, 2021. "Pricing S&P 500 Index Options with L\'evy Jumps," Papers 2111.10033, arXiv.org, revised Nov 2021.
    15. Coutant, Sophie & Jondeau, Eric & Rockinger, Michael, 2001. "Reading PIBOR futures options smiles: The 1997 snap election," Journal of Banking & Finance, Elsevier, vol. 25(11), pages 1957-1987, November.
    16. Chan, Tat Lung (Ron), 2019. "Efficient computation of european option prices and their sensitivities with the complex fourier series method," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    17. Da Silva, M. E. & Guimarães, B. V., 1999. "Precificação de Opções com Volatilidade Estocástica e Saltos," Finance Lab Working Papers flwp_11, Finance Lab, Insper Instituto de Ensino e Pesquisa.
    18. Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July.
    19. Busch, Thomas & Christensen, Bent Jesper & Nielsen, Morten Ørregaard, 2011. "The role of implied volatility in forecasting future realized volatility and jumps in foreign exchange, stock, and bond markets," Journal of Econometrics, Elsevier, vol. 160(1), pages 48-57, January.
    20. Stylianos Perrakis, 2022. "From innovation to obfuscation: continuous time finance fifty years later," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 36(3), pages 369-401, September.

    More about this item

    Keywords

    Barndorff-Nielsen and Shephard Model; Symmetry; Bates’s rule; Ornstein–Uhlenbeck process; C52; G10;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

    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:spr:decfin:v:37:y:2014:i:2:p:319-327. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.