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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

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 Function: First version, 2007
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Bibliographic 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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References

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  1. Peter Carr & Liuren Wu, 2002. "The Finite Moment Log Stable Process and Option Pricing," Finance 0207012, EconWPA.
  2. Robert F. Engle, 1996. "The Econometrics of Ultra-High Frequency Data," NBER Working Papers 5816, National Bureau of Economic Research, Inc.
  3. Enrico Scalas & Rudolf Gorenflo & Francesco Mainardi, 2004. "Fractional calculus and continuous-time finance," Finance 0411007, EconWPA.
  4. Peter Carr & Liuren Wu, 2002. "Time-Changed Levy Processes and Option Pricing," Finance 0207011, EconWPA.
  5. Yacine Ait-Sahalia & Per A. Mykland, 2002. "The Effects of Random and Discrete Sampling When Estimating Continuous-Time Diffusions," NBER Technical Working Papers 0276, National Bureau of Economic Research, Inc.
  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. 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.
  8. 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.
  9. 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.
  10. 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.
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