  A new expression for the characteristic function of log-spot in Heston model
is presented. This expression more clearly exhibits its properties as an
analytic characteristic function and allows us to compute the exact domain of
the moment generating function. This result is then applied to the volatility
smile at extreme strikes and to the control of the moments of spot. We also
give a factorization of the moment generating function as product of Bessel
type factors, and an approximating sequence to the law of log-spot is deduced.
