On the density of log-spot in the Heston volatility model

This paper proves that the log-spot in the Heston model has a C∞C∞ density and gives an expression of this density as an infinite convolution of Bessel type densities. Such properties are deduced from a factorization of the characteristic function, mainly obtained through an analysis of the complex moment generating function. As an application a new algorithm to simulate spot is developed.