Analyzing the Time between Trades with a Gamma Compounded Hazard Model : an Application to LIFFE Bund Future Transactions

Abstract

Kurzfassung: This paper investigates the time between transactions on financial markets. It is assumed that the interval between transactions is a random variable and the relation- ship between the probability to observe a transaction at each instant of time and the type of the previous trade is investigated. To estimate these effects, a semiparametric proportional hazard model is used which is based on approaches proposed by Han and Hausman (1990) and Meyer (1990). Considering grouped durations the log-likelihood is formed by using differences in the survivor function. Hence, the model corresponds to an ordered response approach whereby the baseline hazard is estimated simulta- neously with the coefficients of the covariates and is calculated by the thresholds. Clustering of the durations is taken into account by including lagged durations. A test is proposed to check for serial correlation in the errors based on the concept of generalized residuals along the lines of the work of Gourieroux, Monfort and Trognon (1987). Unobservable heterogeneity is implemented parametrically by a gamma dis- tributed random variable entering the hazard function. It is shown that the resulting compounded model follows a BurrII form. In an empirical analysis high frequency in- traday transaction data from the London International Financial Futures and Options Exchange (LIFFE) is investigated.