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How Duration Between Trades of Underlying Securities Affects Option Prices

Author

Listed:
  • Cartea, Álvaro
  • Meyer-Brandis, Thilo
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 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.

Suggested Citation

  • Cartea, Álvaro & Meyer-Brandis, Thilo, 2009. "How Duration Between Trades of Underlying Securities Affects Option Prices," MPRA Paper 16179, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:16179
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    References listed on IDEAS

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    1. 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.
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    Citations

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    Cited by:

    1. Mengyu Zhang & Thanos Verousis & Iordanis Kalaitzoglou, 2022. "Information and the arrival rate of option trading volume," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(4), pages 605-644, April.
    2. Torricelli, Lorenzo, 2020. "Trade duration risk in subdiffusive financial models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    3. Gurgul Henryk & Machno Artur, 2017. "Trade Pattern on Warsaw Stock Exchange and Prediction of Number of Trades," Statistics in Transition New Series, Statistics Poland, vol. 18(1), pages 91-114, March.
    4. Henryk Gurgul & Robert Syrek & Christoph Mitterer, 2016. "Price duration versus trading volume in high-frequency data for selected DAX companies," Managerial Economics, AGH University of Science and Technology, Faculty of Management, vol. 17(2), pages 241-260.
    5. Álvaro Cartea, 2013. "Derivatives pricing with marked point processes using tick-by-tick data," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 111-123, January.
    6. Antoine Jacquier & Lorenzo Torricelli, 2019. "Anomalous diffusions in option prices: connecting trade duration and the volatility term structure," Papers 1908.03007, arXiv.org, revised Apr 2020.
    7. Syed Mujahid Hussain & Sergey Osmekhin & Frédéric Délèze, 2021. "Short-term market efficiency indicator based on the waiting-time distribution," Review of Managerial Science, Springer, vol. 15(6), pages 1561-1572, August.
    8. Vasily E. Tarasov, 2019. "On History of Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 7(6), pages 1-28, June.

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    More about this item

    Keywords

    Duration between trades; waiting-times; stochastic volatility; operational clock; transaction time; high frequency data.;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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