Another approach of financial modelling based on poisson distribution with conditional intensity

Abstract

Stochastic processes with conditional heteroscedasticity have been widely used to model time-varying volatility since Engle established the ARCH model. This paper provides stochastic processes based on Poisson distribution with conditional intensity under the several assumptions more compatible with real economic phenomena than ARCH or GARCH models. In this paper, several possible modeling for intensity functions are given and its quantitative properties are derived. Simulations are proposed to be compared with empirical data. In the final section, we link the our models with L$\acute{e}$vy process theory and show the existence of risk neutral probability.