Suppose you are given the following data:
• Risk-free interest rate is 6%
• The stock price follows:
dSt = μSt + σStdWt
Volatility is 12 % a year
• The stock pays no dividends anti the current stock price is 100.
Using these data you are asked to approximate the current value of an American call option on the stock. The option has a strike price of 100 and a maturity of 200 days.
(a) Determining an appropriate time interval ?, such that the binomial tree has four steps. What would be the implied U and D?
(b) What is the implied "up" probability?
(c) Determine the tree for the stock pit St.
(d) Determine the tree for the call premium Ct.
(e) Now the important question: would this option ever he exercised early?