How Duration Between Trades of Underlying Securities Affects Option Prices
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.
|Date of creation:||22 Apr 2009|
|Date of revision:|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
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.:
- repec:dau:papers:123456789/1392 is not listed on IDEAS
- Enrico Scalas & Rudolf Gorenflo & Francesco Mainardi, 2000.
"Fractional calculus and continuous-time finance,"
- Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
- 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.
- 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.
- Peter Carr & Liuren Wu, 2002.
"The Finite Moment Log Stable Process and Option Pricing,"
- Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-778, 04.
- 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.
- 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.
- 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.
- Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2000.
"Fractional calculus and continuous-time finance II: the waiting-time distribution,"
cond-mat/0006454, arXiv.org, revised Nov 2000.
- Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
- Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2004. "Fractional calculus and continuous-time finance II: the waiting- time distribution," Finance 0411008, EconWPA.
- 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.
- Bossaerts, P. & Ghysels, E. & Gourieroux, C., 1996. "Arbitrage-Based Pricing when Volatility is Stochastic," Cahiers de recherche 9615, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Peter Bossaert & Eric Ghysels & Christian Gouriéroux, 1996. "Arbitrage Based Pricing When Volatility Is Stochastic," CIRANO Working Papers 96s-20, CIRANO.
- Bossaerts, Peter & Ghysels, Eric & Gourieroux, Christian, 1996. "Arbitrage-Based Pricing When Volatility is Stochastic," Working Papers 977, California Institute of Technology, Division of the Humanities and Social Sciences.
- 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.
- 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.
- 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.
- 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.
- Tauchen, George E & Pitts, Mark, 1983. "The Price Variability-Volume Relationship on Speculative Markets," Econometrica, Econometric Society, vol. 51(2), pages 485-505, March.
- 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.
- 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.
- 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.
- 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.
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 references are entirely missing, you can add them using this form.