I am attempting to calculate the Greeks, and I understand their derivation. However when it comes to actually implementing Vega I am a little lost. Vega is defined analytically as:
$$ SN'(d_1)\sqrt{T-t} $$
It seems that it requires the first derivative of a normal distribution. I thought my probability knowledge was ok but I can't seem to find anything about its behavior, or how to implement the first derivative of a normal distribution programmatically.
Can anyone help me understand this?
Thank you!