Statistical Analysis of Absolute Transaction Price Changes of Options

In market microstructure theory the effect of time between
consecutive transactions and trade volume on transaction price
changes of exchange traded shares and options has been considered
(e.g. Diamond and Verecchia (1987) and Easley and O'Hara (1987)).
The goal of this paper is to investigate if these theoretical
considerations can be supported by a statistical analysis of data
on transaction price changes of options on shares of the Bayer AG
in 1993-94. For this appropriate regression models with non linear
and interaction effects are developed to study the influence of
trade volume, time between trades, intrinsic value of an option at
trading time and price development of the underlying share on the
absolute transation price change of an option. Since price changes
are measured in ticks yield count data structure, we use in a first
analysis ordinary Poisson generalized linear models (GLM) ignoring
the time series structure of the data. In a second analysis these
Poisson GLM's are extended to allow for an additional AR(1) latent
process in the mean which accounts for the time series structure.
Parameter estimation in this extended model is not straight forward
and we use Markov Chain Monte Carlo (MCMC) methods. The extended
Poisson GLM is compared to the ordinary Poisson GLM in a Bayesian
setting using the deviance information criterion (DIC) developed by
Spiegelhalter et al. (2002). With regard to market microstructure
theory the results of the analysis support the expected effect of
time between trades on absolute option price changes but not for
trade volume in this data set.