Thoughts about Ito Lemma and Black Scholes Model

ito lemma is a very lengthy formula. To highlight the key points as the following:

1. Remember bivariate Taylor expansion
2. Remember (dS)^2=b^2*dt
3. Remember (dWt)^2=dt

the Black Scholes formula says that the price of an option, before discounting, equals the expected value of receiving the stock in the event of exercise (F*N[d1]) minus the cost of paying the strike price in the event of exercise (K*N[d2]).

So you can think of N[d2] as the probability of exercise (that is, paying the strike price), and N[d1] a measure how far in the money the option is expected to be if it does expire in the money, roughly speaking. 

N(d2) 是执行概率
N(d1) 是moneyness的深度