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by Eric Ghysels and Joanna Jasiak Abstract We develop a class of ARCH models for series sampled at unequal time intervals set by trade or quote arrivals. Our approach combines insights from the temporal aggregation for GARCH models discussed by Drost and Nijman (1993) and Drost and Werker (1994), and the autore- gressive conditional duration model of Engle and Russell (1996) proposed to model the spacing between consecutive nancial transactions. The class of models introduced here will be called ACD-GARCH. It can be described as a random coe cient GARCH, or doubly stochastic GARCH, where the durations between transac- tions determine the parameter dynamics. The ACD-GARCH model becomes genuinely bivariate when past asset return volatilities are allowed to a ect transaction durations and vice versa. Otherwise the spacings between trades are considered exogenous to the volatility dynamics. This assumption is required in a two-step estimation procedure. The bivariate setup enables us to test for Granger causality between volatility and intra-trade durations. Under general conditions we propose several GMM estimation procedures, some having a QMLE interpreta- tion. As illustration we present an empirical study of the IBM 1993 tick-by-tick data. We nd that volatility of IBM stock prices Granger causes intra-trade durations. We also nd that the persistence in GARCH drops dramatically once intra-trade durations are taken into account. Discuss this paper
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describes a pratical example of using it to analyse data. theory is not much detailed but you get the idea of what all is involed even to run the GUI Discuss this paper
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Yoshio Miyahara Nagoya City University Alexander Novikov University of Technology Sydney Abstract We consider models for stock prices which relates to random processes with independent homogeneous increments Levy processes These models are arbitrage free but correspond to the incomplete financial market There are many dierent approaches for pricing of nancial derivatives We consider here mainly the approach which is based on minimal relative entropy This method is related to an utility function of exponential type and the Esscher transformation of probabilistic measures
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