The volatility of a non-dividend-paying stock whose price is $78, is 30%. The risk-free rate is

3% per annum (continuously compounded) for all maturities. Calculate the following when a

2-month time step is used:

a. What is the percentage up movement?

b. What is the percentage down movement?

c. What is the probability of an up movement in a risk-neutral world?

d. What is the probability of a down movement in a risk-neutral world?

e. What is the value a 4-month European call option with a strike price of $80 given by

a two-step binomial tree? Draw your binomial tree