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 model 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 transaction 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.