4. (American Option Pricing)

In this exercise we use the binomial method to price American options. Answer the following questions:

a) Compute the price of an American option for large values of the expiration T, for example T in the range [10, 100] years in steps of 10 years. How many time steps are needed in order to achieve convergence in each case?

b) For which expiration value T does the binomial method give the same value as the formulae (12.9) and (12.10) for a perpetual American option (if at all)?