IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

Short and Long Term Smile Effects: The Binomial Normal Mixture Diffusion Model

Listed author(s):
  • Carol Alexander


    (ICMA Centre, University of Reading)

This paper extends the normal mixture diffusion (NMD) local volatility model of Brigo and Mercurio (2000, 2001a,b, 2002) so that it explains both short-term and long-term smile effects. Short-term smile effects are captured by a local volatility model where excess kurtosis in the price density decreases with maturity. This follows from the central limit theorem and concords with the ‘stylised facts’ of econometric analysis of ex-post returns of different frequencies. We introduce a term structure for option prices in the NMD model by assuming there is a fixed probability of each volatility state occurring in every time interval Dt, and we show that with this assumption the mixing law for the price density is the multinomial density. This very parsimonious model can easily be calibrated to observed option prices. However, smile effects in currency options often persist into fairly long maturities, and to capture at least some part of this it is necessary to introduce stochastic volatility. The last part of this paper considers only two possible volatility states in each Dt with probabilities l and (1 - l). If l were fixed, the binomial mixing law model would only apply to short-term smile effects. But by making l stochastic, longer-term smile effects that arise from uncertainty in volatility are also captured by the model. The results are illustrated by calibrating the model with and without stochastic l, to a currency option smile surface

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: no

Paper provided by Henley Business School, Reading University in its series ICMA Centre Discussion Papers in Finance with number icma-dp2003-06.

in new window

Length: 24 pages
Date of creation: Nov 2002
Date of revision: Mar 2003
Publication status: Published in Journal of Banking and Finance 2004, 28:12, 2957-2980
Handle: RePEc:rdg:icmadp:icma-dp2003-06
Contact details of provider: Postal:
PO Box 218, Whiteknights, Reading, Berks, RG6 6AA

Phone: +44 (0) 118 378 8226
Fax: +44 (0) 118 975 0236
Web page:

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

in new window

  1. Damiano Brigo & Fabio Mercurio & Giulio Sartorelli, 2003. "Alternative asset-price dynamics and volatility smile," Quantitative Finance, Taylor & Francis Journals, vol. 3(3), pages 173-183.
  2. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
  3. 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.
  4. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
  5. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
  6. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
  7. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:rdg:icmadp:icma-dp2003-06. 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)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.