IDEAS home Printed from https://ideas.repec.org/p/rdg/icmadp/icma-dp2001-10.html
   My bibliography  Save this paper

Option Pricing with Normal Mixture Returns: Modelling Excess Kurtosis and Uncertanity in Volatility

Author

Listed:
  • Carol Alexander

    () (ICMA Centre, University of Reading)

  • Sujit Narayanan

    () (ICMA Centre, University of Reading)

Abstract

his paper addresses the problem of uncertainty in volatility, and how this affects option prices. The volatility uncertainty adjustment to Black-Scholes option prices is quantified in this paper using a normal mixture model for the distribution of underlying returns, or equivalently, assuming a mixture of lognormal densities for the density of the asset price. The use of a lognormal mixture price process for pricing options is not new (Ritchey, 1990) but the local volatility that should be used in the lognormal mixture price process has only recently been established (Brigo and Mercurio, 2000a, 2001).

Suggested Citation

  • Carol Alexander & Sujit Narayanan, 2001. "Option Pricing with Normal Mixture Returns: Modelling Excess Kurtosis and Uncertanity in Volatility," ICMA Centre Discussion Papers in Finance icma-dp2001-10, Henley Business School, Reading University, revised Dec 2001.
  • Handle: RePEc:rdg:icmadp:icma-dp2001-10
    as

    Download full text from publisher

    File URL: http://www.icmacentre.ac.uk/pdf/discussion/DP2001-10.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Ritchey, Robert J, 1990. "Call Option Valuation for Discrete Normal Mixtures," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 13(4), pages 285-296, Winter.
    2. Baillie, Richard T & Bollerslev, Tim, 2002. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 60-68, January.
    3. Kien Tran, 1998. "Estimating mixtures of normal distributions via empirical characteristic function," Econometric Reviews, Taylor & Francis Journals, pages 167-183.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, pages 307-327.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, pages 307-327.
    6. Goodhart, Charles A. E. & O'Hara, Maureen, 1997. "High frequency data in financial markets: Issues and applications," Journal of Empirical Finance, Elsevier, pages 73-114.
    7. Hsieh, David A., 1988. "The statistical properties of daily foreign exchange rates: 1974-1983," Journal of International Economics, Elsevier, pages 129-145.
    8. Muller, Ulrich A. & Dacorogna, Michel M. & Olsen, Richard B. & Pictet, Olivier V. & Schwarz, Matthias & Morgenegg, Claude, 1990. "Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis," Journal of Banking & Finance, Elsevier, vol. 14(6), pages 1189-1208, December.
    9. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
    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. Kole, H.J.W.G. & Koedijk, C.G. & Verbeek, M.J.C.M., 2004. "The effects of systemic crises when investors can be crisis ignorant," ERIM Report Series Research in Management ERS-2004-027-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    2. En-Der Su & Feng-Jeng Lin, 2012. "Two-State Volatility Transition Pricing and Hedging of TXO Options," Computational Economics, Springer;Society for Computational Economics, vol. 39(3), pages 259-287, March.
    3. Damiano Brigo, 2008. "The general mixture-diffusion SDE and its relationship with an uncertain-volatility option model with volatility-asset decorrelation," Papers 0812.4052, arXiv.org.
    4. Fleming, Jeff & Paye, Bradley S., 2011. "High-frequency returns, jumps and the mixture of normals hypothesis," Journal of Econometrics, Elsevier, pages 119-128.

    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:rdg:icmadp:icma-dp2001-10. 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: (Marie Pearson). General contact details of provider: http://edirc.repec.org/data/bsrdguk.html .

    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 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.