How Duration Between Trades of Underlying Securities Affects Option Prices Articles
Overview
published in
- Review of Finance Journal
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)
- 1573-692X
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.