2. Suppose you are given the following data:

The risk-free interest rate is 6%.

The stock price follows:

dSt 5 μSt dt 1 σSt dWt (8.83)

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? Hint: To obtain the probability we need to discretize the stochastic differential equation.

c. Determine the tree for the stock price St.

d. Determine the tree for the call premium Ct.