Question: Suppose you are given the following data:
• The risk-free interest rate is 6%.
• The stock price follows:
dSt = μSt dt + σSt dWt
• Volatility is 12% a year.
• The stock pays no dividends and the current stock price is 100. Using these data, you are asked to approximate the current value of a European call option on the stock. The option has a strike price of 100 and a maturity of 200 days.
a. Determine an appropriate time interval Δ, such that an implied binomial tree has five steps.
b. What is the implied up probability?
c. Determine the tree for the stock price St.
d. Determine the tree for the call premium Ct.