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 put option on the stock has exercise price $90 and expires in one year. Denote the price of this put option today as P put and then Pu,Pd, and, Puu, Pud, Pdu, Pdd the payoffs after 6 months and 1 year respectively. Calculate Puu, Pud, Pdu, Pdd.
C. Find the price of such a put option by using the replication method of a call option. Assume the 6-month risk-free interest rate is 2 percent