How Duration Between Trades of Underlying Securities Affects Option Prices

49 Pages Posted: 27 Nov 2007 Last revised: 11 Mar 2013

See all articles by Álvaro Cartea

Álvaro Cartea

University of Oxford; University of Oxford - Oxford-Man Institute of Quantitative Finance

Thilo Meyer-Brandis

University of Oslo

Date Written: November 1, 2007

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 his 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 olatility decreases in the presence of longer durations, a result consistent with the findings of Engle (2000) and Dofour and Engle (2000) which demonstrates the relationship between levels of activity and volatility for stock prices. Finally, by directly employing information given by time- tamps of trades, our approach provides a direct link between the literature on stochastic time hanges 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.

Keywords: Duration between trades, waiting-times, stochastic volatility, operational clock, transaction time, high frequency data

JEL Classification: G12, G13

Suggested Citation

Cartea, Álvaro and Meyer-Brandis, Thilo, How Duration Between Trades of Underlying Securities Affects Option Prices (November 1, 2007). Review of Finance, Volume 14, Issue 4, October 2010, p 749-785, Available at SSRN: https://ssrn.com/abstract=1032714

Álvaro Cartea (Contact Author)

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

Thilo Meyer-Brandis

University of Oslo ( email )

PO Box 6706 St Olavs plass
Oslo, N-0317
Norway

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