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

Inputs of Black Scholes Formula

Describe the three classes of inputs to the Black-Scholes formula, setting out the members of each class and the type of risks associated with each class (note: not each member).

1. Market Data => market risk

spot price

interest rate

2. Contract Data => ? risk

strike

tenor

3. Model Parameter => model risk

Volatility