An investor wants to compare premium prices of a European call calculated with the BlackScholes model with premium prices calculated with a binomial model. The call has strike price K = $19 and the underlying asset is currently selling for S = $20 . The yearly volatility of the underlying is estimated to be = 0.55 . The interest rate is r = 6% pa. The call expires in 90 days so T = 90/365 years.

(a) Calculate the call premium using the BlackScholes model.

(b) Consider a three-step binomial model.

(i) Assuming interest rates are constant over the life of the call, calculate the return R over one time step.

(ii) Calculate the up and down factors u and d in this three-step model.

(iii) Calculate the risk neutral probability in this three-step model.

(iv) Construct a three-step binomial pricing tree for the call and calculate its premium.