Can anyone give a detailed concept of Binomial, Black Scholes Merton, Geometric Brownian Motion, Monte CArlo for Valuation? Which is applicable in which circumstances?

I'm taking Level 1 this year so I'm not sure if all will be tested and I'm pretty confused by them.

My understanding is:

Binomial

Simply probabilities of up and down

e-2rt (p2U + 2p(1-p)UD + (1-p)2D) = option price

Black Scholes Merton

- Include lognormal properties

d1 = [ln (S/K) + (r+σ2/2)T] ÷σ√T

d2 = [ln (S/K) + (r-σ2/2)T] ÷σ√T = d1 - σ√T

CALL PRICE = S0N(d1) – Ke -rT N(d2)

PUT PRICE = Ke -rT N(-d2) - S0N(-d1)

Monte Carlo

- Factors into stochastic part of price mvmt

which formula do I need to memorize?

Geometric Brownian Motion

- no idea?

Thanks!