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

a) Consider a ten step binomial model. Assuming interest rates are constant over the life of the call, calculate the return R over one time step. Then, calculate the up and down factors u and d in this ten step model. Also, calculate the risk neutral probability in this ten step model. Finally, construct a ten step binomial tree for the call and calculate its premium.