Reconciliation of Black-Scholes Variants
This note is just to show that the different variants of Black-Scholes formula in textbook and tutorial solutions are in fact the same.
: Underlying share price : Time to maturity : Standard deviation of underlying share price : Exercise price : Risk-free rate
Variant 1
This is the one shown in our formula sheet, and is also the traditional presentation of Black-Scholes model.
Variant 2
This one comes from textbook, and looks slightly different in that
However, itβs in fact easy to show that
Therefore, the two variants are effectively the same under continuous compounding.