1 Sigma

Comparing NormalDistribution vs LognormalDistribution:

Code:

Using NormalDistribution:
ExpectedMove for S=100.0000 Vola=30.0000 nDays=365.00 z=-1.00 rPct=0.0000 qPct=0.0000 : -30.000000(-30.0000% --> Sx=70.000000)
ExpectedMove for S=100.0000 Vola=30.0000 nDays=365.00 z=+1.00 rPct=0.0000 qPct=0.0000 : +30.000000(+30.0000% --> Sx=130.000000)

Using LognormalDistribution:
ExpectedMove for S=100.0000 Vola=30.0000 nDays=365.00 z=-1.00 rPct=0.0000 qPct=0.0000 : -25.918178(-30.0000% --> Sx=74.081822)
ExpectedMove for S=100.0000 Vola=30.0000 nDays=365.00 z=+1.00 rPct=0.0000 qPct=0.0000 : +34.985881(+30.0000% --> Sx=134.985881)