Please assist with the given problem about international trade. Provide step by step calculations in the solution.
You observe that a non-dividend paying stock, with a current price of $50, has 1-year American calls and puts written on it, both with exercise prices of $50. The 1-year interest rate is 10%.
(1) If the calls were trading at $10 and the puts at $3, what trades would you enter into?
(2) If the calls were trading at $5 and the puts at $5, what trades would you enter into?
[Hint: an important thing in Q#2 is to determine whether you will (or will not) enter into such trades and why (or why not)]