Before revision:  The advantages are that for the mean-reverting square-root process in the Heston model and Cox-Ingersoll-Ross model, we can generate samples from the true transition density simply, efficiently and robustly .
After revision:  The advantages are that for the mean-reverting square-root process in the Heston model . We focus on the case when the number of degrees of freedom is small and the zero boundary is attracting and attainable, typical in foreign exchange markets. Using the additivity property of the chi-square distribution, our methods apply in all parameter regimes .