A micro-to-macro approach to returns, volumes and waiting times

Modelling stock prices has been a research topic for many decades and it is still an open question. Different approaches have been used in the literature, the majority of which can be classified within the so-called econometric framework and sometimes also referred to as the macro-to-micro approach. Another strand of literature relies on the modelling of directly observable quantities, the so-called micro-to-macro approach. Based on this second line of research, we propose a new multivariate stochastic process to model simultaneously price returns, trading volumes and the time interval between changes in trades, price and volume. The proposed model is based on a generalization of semi-Markov chain models and copulas and is motivated by empirical evidence that the three mentioned variables are correlated and long-range autocorrelated. Utilizing Monte Carlo simulations, we compared our model with real data from the Italian stock market and show that it can reproduce many empirical pieces of evidence. The proposed model can be used in the field of portfolio optimization, development of risk measure and volatility forecasting.