# Why do simulation schemes have difficulty in pricing options with low spots?

If you apply a simulation Scheme (log-Euler discretization, Euler discretization and even more advanced ones) on for instance SABR and other models, then they price a call option (where we can easy compute the theoretical value for SABR at least) significantly better when spot is high rather than small. When spot gets closer to zero then the prices from simulations gets more wrong.

For instance, even the more advanced simulations presented in: http://ta.twi.tudelft.nl/mf/users/oosterle/oosterlee/SABRMC.pdf

prices options better for spot = 10 rather than spot = 0.1 (all else being equal) with strike = 95%spot.

Why is that generally the case?