IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

How Duration Between Trades of Underlying Securities Affects Option Prices

  • Cartea, Álvaro
  • Meyer-Brandis, Thilo

We propose a model for stock price dynamics that explicitly incorporates random waiting times between trades, also known as duration, and show how option prices can be alculated using this model. We use ultra-high-frequency data for blue-chip companies to motivate a particular choice of waiting-time distribution and then calibrate risk- eutral parameters from options data. We also show that the convexity commonly observed in implied volatilities may be explained by the presence of duration between trades. Furthermore, we find that, ceteris paribus, implied olatility decreases in the presence of longer durations, a result consistent with the findings of Engle (2000) and Dufour and Engle (2000) which demonstrates the relationship between levels of activity and volatility for stock prices. Finally, by directly employing information given by time-stamps of trades, our approach provides a direct link between the literature on stochastic time changes and business time (see Clark (1973)) and, at the same time, highlights the link between number and time of arrival of transactions with implied volatility and stochastic volatility models.

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: https://mpra.ub.uni-muenchen.de/16179/1/MPRA_paper_16179.pdf
File Function: original version
Download Restriction: no

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 16179.

as
in new window

Length:
Date of creation: 22 Apr 2009
Date of revision:
Handle: RePEc:pra:mprapa:16179
Contact details of provider: Postal:
Ludwigstraße 33, D-80539 Munich, Germany

Phone: +49-(0)89-2180-2459
Fax: +49-(0)89-2180-992459
Web page: https://mpra.ub.uni-muenchen.de

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.:

as in new window
  1. Enrico Scalas & Rudolf Gorenflo & Francesco Mainardi, 2004. "Fractional calculus and continuous-time finance," Finance 0411007, EconWPA.
  2. Bossaerts, P. & Ghysels, E. & Gourieroux, C., 1996. "Arbitrage-Based Pricing when Volatility is Stochastic," Cahiers de recherche 9615, Universite de Montreal, Departement de sciences economiques.
  3. Epps, Thomas W & Epps, Mary Lee, 1976. "The Stochastic Dependence of Security Price Changes and Transaction Volumes: Implications for the Mixture-of-Distributions Hypothesis," Econometrica, Econometric Society, vol. 44(2), pages 305-21, March.
  4. repec:dau:papers:123456789/1392 is not listed on IDEAS
  5. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
  6. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
  7. Easley, David & O'Hara, Maureen, 1992. " Time and the Process of Security Price Adjustment," Journal of Finance, American Finance Association, vol. 47(2), pages 576-605, June.
  8. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1992. "Stock Prices and Volume," Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 199-242.
  9. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January.
  10. Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Papers cond-mat/0006454, arXiv.org, revised Nov 2000.
  11. Andersen, Torben G, 1996. " Return Volatility and Trading Volume: An Information Flow Interpretation of Stochastic Volatility," Journal of Finance, American Finance Association, vol. 51(1), pages 169-204, March.
  12. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
  13. Dufour, Alfonso & Engle, Robert F, 1999. "Time and the Price Impact of a Trade," University of California at San Diego, Economics Working Paper Series qt62c0h04j, Department of Economics, UC San Diego.
  14. Tauchen, George E & Pitts, Mark, 1983. "The Price Variability-Volume Relationship on Speculative Markets," Econometrica, Econometric Society, vol. 51(2), pages 485-505, March.
  15. Jones, Charles M & Kaul, Gautam & Lipson, Marc L, 1994. "Transactions, Volume, and Volatility," Review of Financial Studies, Society for Financial Studies, vol. 7(4), pages 631-51.
  16. Peter Carr & Liuren Wu, 2002. "The Finite Moment Log Stable Process and Option Pricing," Finance 0207012, EconWPA.
  17. Karpoff, Jonathan M., 1987. "The Relation between Price Changes and Trading Volume: A Survey," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(01), pages 109-126, March.
  18. Diamond, Douglas W. & Verrecchia, Robert E., 1987. "Constraints on short-selling and asset price adjustment to private information," Journal of Financial Economics, Elsevier, vol. 18(2), pages 277-311, June.
  19. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
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:pra:mprapa:16179. 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: (Joachim Winter)

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.