Abstract
Firstly, the asynchronous discrete cadlag feature of price and order time series demands causal structuring.
We determine the waiting time between two successive market events by an approach that might
be named doubly stochastic Markov process, analogously to doubly stochastic Poisson process. The assumption
of a time-continuous and -homogeneous conservative Markov process leads to waiting times
following an exponential distribution. Its state dependent parameter is governed by the dynamics of
the Markov process. Secondly, in our model the state transition is not constant, but controlled by the
probability that the acting agent takes the action which generates the transition. Thirdly, the probability
for placing buy or sell orders is determined according to the willingness to pay concept of discrete
choice models based on random utility. The causal foundation of the model relies on the basic principle:
The higher the utility of an activity, the higher the probability of taking this activity, and the shorter the
expected waiting time. Simulated price and order time series are presented.
Keywords: Doubly Stochastic Markov Process; Random Utility Maximization; Interacting agents; Market
Microstructure; Order book simulation; Quantitative-Behavioural Finance