This question asks you to apply your knowledge on option securities. Suppose the price of a stock is $100 today and it evolves according to u = 1.1 and d = 0.8 in 6-month periods.
A. Draw and label a tree that shows the price of the stock today, after 6-months and after 1 year.
B. A call option on the stock has exercise price $90 and expires in one year. Denote the price of this call option today as Pcall and then Cu, Cd, and Cuu, Cud, Cdu, Cdd the payoffs after 6 months and 1 year respectively. Calculate Cuu, Cud, Cdu, Cdd.
C. Find the price of such a call option when the 6-month risk-free interest rate is 2 percent.
D. Find the price of a put option on the stock with the same exercise price as the call and expiration date after 1 year.
E. Now suppose that the price of the stock after 1 year can take any positive value. A strip is a portfolio consisting of buying one call and two put options on the same stock with the same exercise price and expiration. Draw the payoff and the profit of a strip as a function of S1, where the call and put exercise prices and prices are those you found above. Write the payoff and the profit of a strap as piece-wise functions.