Suppose we are to price with Monte Carlo method two options differing only in the maturity time, with the same, say, call option payoff, or Asian option payoff with a fixed averaging window, with the underlying stock price following the Heston model. We know the distribution of variance in the Heston model approaches a stationary one as time approaches infinity. To achieve the same accuracy,
1) can we use longer time step size for the option with longer maturity than the one with shorter maturity?
2) What about using variable time step size with step size growing towards the time of maturity?