  In an asset return series there is a conditional asymmetric dependence
between current return and past volatility depending on the current return's
sign. To take into account the conditional asymmetry, we introduce new models
for asset return dynamics in which frequencies of the up and down movements of
asset price have conditionally independent Poisson distributions with
stochastic intensities. The intensities are assumed to be stochastic recurrence
equations of the GARCH type in order to capture the volatility clustering and
the leverage effect. We provide an important linkage between our model and
existing GARCH, explain how to apply maximum likelihood estimation to determine
the parameters in the intensity model and show empirical results with the S&P
500 index return series.
