The Dynamic Mixed Hitting-Time Model for Multiple Transaction Prices and Times

Abstract

We propose a structural model for durations between events and (a vector of) associated marks, using a multivariate Brownian motion. Successive passage times of one latent Brownian component relative to random boundaries define durations. The other, correlated, Brownian components generate the marks. Our model embeds the class of stochastic conditional (SCD) and autoregressive conditional (ACD) duration models, which impose testable restrictions on the relation between the conditional expectation and conditional volatility of durations. We strongly reject the SCD and ACD specifications for both a very liquid and less liquid NYSE-traded stock, and characterise causality relations between volatilities and durations.

Keywords: duration modeling, hitting time, trading intensity, market microstructure

JEL Classification: C41, G12