How Duration Between Trades of Underlying Securities Affects Option Prices Articles uri icon

authors

  • CARTEA GONZALEZ, ALVARO IVAN
  • MEYER BRANDIS, THILO

publication date

  • October 2010

start page

  • 749

end page

  • 785

issue

  • 4

volume

  • 14

International Standard Serial Number (ISSN)

  • 1572-3097

Electronic International Standard Serial Number (EISSN)

  • 1875-824X

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.