This question asks you to apply your knowledge on option securities.
(a) Suppose the price of a stock today is $40 and it evolves according to u = 1.1 and d = 0.9 in 6-month periods. A call option on the stock expires after 1 year and has exercise price $42. Find the prices and the payoffs of the stock and call respectively for each possible scenario.
(b) Use the Binomial Model to finnd the price of this call if the 6 month risk free interest rate is 2 percent.
(c) Find the price of a put option with exercise price $42 that expires after 1 year.
(d) Now suppose that the price of the stock after 1 year can take any positive value. A collar is a portfolio consisting of a stock, buying a put on the stock and writing a call on the stock. The put exercise price is $42 and the call exercise price is $44. Prices of the call and put are what you found in (b) and (c). Write the payoff of the collar as a piece-wise function.
(e) Write the profit of the collar described above as a piece-wise function.
(f) Draw the payoff of the collar described above as a function of S1.
(g) Draw the profit of the collar described above as a function of S1.