The stock of the Miami Tower Company (MTC) is currently worth $100. Over each of the next two years, the stock price will either move up to 115% of the beginning-of-year stock price or down to 90% of the beginning of year price.
You do not know which one will happen, nor how likely these are. The risk-free interest rate is 3% per year. MTC will also pay a $2 per share dividend at the end of year 1.
Assume that it is possible to observe the stock price at the end of year 1, exercise any option you might hold immediately (should you choose to do so), and still qualify for the dividend if exercise gives ownership of the underlying.
(a) What is the price of a two-year European Call Option with strike price $95, written on MTC stock?
(b) What is the price of a two-year American Call Option with strike price $95, written on MTC stock? For full credit, you must show whether early exercise is profitable in each state of the world.
(c) What is the price of a two-year American Put Option with strike price $95, written on MTC stock? For full credit, you must show whether early exercise is profitable in each state of the world.
(d) What is the price of a two-year American Put Option with strike price $105, written on MTC stock?