Binomial Option Pricing, Black Scholes Option Pricing

5) Binomial Option Pricing: Suppose we live in a 3 period Black-Scholes world, t=0,1,2 whichidentify as follows. There is a stock with price S(0)= 1 in period 0.In each period , t=1,2, the price can either go up to u. S or down to d.S.
Suppose u=1.2 and d=0.9. Suppose that the interest rate is constant at 4%.
A) What is the period 0 price of a European call option with strike X =1 and expiration t=2? What is the price of a European put option with strike X =1 and expiration t=2?"

Recall that American option can be exercised at any date before (an including) their expiration date. Can you say anything about the price of an American call option with strike X =1 and expiration t=2?

6. Black Scholes Option Pricing: On March 4 of some year the North bay Company's September 48 call option is selling for $4, The stock itself is selling for $49. On March 4, the option has 201 days to expiration since the maturity date of the option was September 21 of that same year. The annual risk free rate with continuous compounding was 4% on march 4. Econometric estimates on the stock returns show that the variance of the return on North Bay stock is 0.08 per year.

What does the Black-Scholes option pricing formula predict the price of the call option should be? How would you explain the difference between this price and actual market price of $4?