Consider a call option for an asset with the following parameters:

Current spot price is $50

Option expires in 12 months

Each month the asset could increase in value by 3% or decrease in value by inverse.

The risk free rate is 25 basis points per month.

So = $50, T = 12, U = 1.03, D = 1/1.03, r = 0.0025 = 0.25%

The strike is $55.

a. Find the terminal distribution of the asset price.

b. Describe the distribution (mean, standard deviation, shape......) Remember to use the probabilities to calculate mean, variance and standard deviation.

c. What do you expect to spend to buy the underlier (assume $0 if not exercised) and what is the present value?

d. What do you expect to receive from selling the underlier (assume $0 if not exercised) and what is the present value?

e. Combine your answers to part c and d to calculate the premium of a call option with strike $55 (10% otm) expiring in 12 months.