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How Does Duration Between Trades of Underlying Securities Affect Option Prices

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Author Info
Alvaro Cartea (Department of Economics, Mathematics & Statistics, Birkbeck)
Thilo Meyer-Brandis

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Abstract

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 calculated 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-neutral 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 volatility 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.

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File URL: http://www.ems.bbk.ac.uk/research/wp/PDF/BWPEF0721.pdf
File Format: application/pdf
File Function: First version, 2007
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Publisher Info
Paper provided by Birkbeck, Department of Economics, Mathematics & Statistics in its series Birkbeck Working Papers in Economics and Finance with number 0721.

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Date of creation: Dec 2007
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Handle: RePEc:bbk:bbkefp:0721

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Related research
Keywords: Duration between trades; waiting-times; high frequency data; Levy processes; option pricing; time changes; operational time; irregularly spaced data.;

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  1. Robert F. Engle, 2000. "The Econometrics of Ultra-High Frequency Data," Econometrica, Econometric Society, vol. 68(1), pages 1-22, January.
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  2. Enrico Scalas & Rudolf Gorenflo & Francesco Mainardi, 2004. "Fractional calculus and continuous-time finance," Finance 0411007, EconWPA. [Downloadable!]
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  3. Peter Carr & Liuren Wu, 2002. "Time-Changed Levy Processes and Option Pricing," Finance 0207011, EconWPA. [Downloadable!]
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  4. Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Quantitative Finance Papers cond-mat/0006454, arXiv.org, revised Nov 2000. [Downloadable!]
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  5. Yacine Ait--Sahalia & Per A. Mykland, 2003. "The Effects of Random and Discrete Sampling when Estimating Continuous--Time Diffusions," Econometrica, Econometric Society, vol. 71(2), pages 483-549, March. [Downloadable!] (restricted)
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  6. 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.
  7. 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. [Downloadable!] (restricted)
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  8. Alfonso Dufour & Robert F. Engle, 2000. "Time and the Price Impact of a Trade," Journal of Finance, American Finance Association, vol. 55(6), pages 2467-2498, December. [Downloadable!] (restricted)
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  9. 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. [Downloadable!] (restricted)
  10. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April. [Downloadable!]
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