The price of a non-dividend paying stock is now $40. Over each of the next two three-month periods, it is expected to go up by 10% or down by 10%. The risk-free interest rate is 4% per annum with continuous compounding.

a. Calculate the risk-neutral probability p of an up-move over each three-month period

b. Calculate the value of a six-month European call option with a strike price of $42

c. Calculate the value of a six-month European put option with a strike price of $42

d. If the six-month put option was American instead of European, how would you expect its value to be different (higher, the same, or lower) than the European one? Please explain