Publication: How duration between trades of underlying securities affects option prices
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2009-05-21
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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. 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
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Duration between trades, Waiting-times, Stochastic volatility, Operational clock, Transaction time, High frequency data