Review of Finance Advance Access published online on July 17, 2009
Review of Finance, doi:10.1093/rof/rfp013
How Duration Between Trades of Underlying Securities Affects Option Prices*
1 Universidad Carlos III de Madrid
2 University of Oslo
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.
JEL Classification: G12, G13
* This paper has benefited from comments of seminar participants at The University of Chicago, Federal Reserve Bank Chicago, University of Florence, University of Toronto, University of Oxford, ESSEC, King's College London, Birkbeck-University of London and Universidad Carlos III de Madrid. For comments and suggestions on earlier drafts, we are indebted to G. Amromin, L. Benzoni, R. Brummelhuis, M.G. Figueroa, C. Furfine, H. Geman, S. Howison, A. Ihlan, S. Jaimungal, T. Jenkinson, P. Kyle, D. Marshall, D. Madan, C. Mayer, R. McDonald, R. Oomen, A. Roncoroni, O. Sussman and J. van Bommel. We are also grateful to Peter Bossaerts (the editor) and an anonymous referee for very insightful and useful comments.