Estimate the values of the derivatives with the following characteristics using Binomial Trees with 20 steps (time steps). a. European and American call options with underlying asset IBM stock with today price S0=$60, strike price X=59, risk-free rate r=6%, dividend yield d=4% and time to maturity T=1. volatility of the stock = 23.7%. What do you notice? What would we observe if d=0?

b.A compound option is an option with an underlying asset another option with a different one underlying asset (option on option). The exercise price of a compound option is function of the value of the other option. Thus there are 2 strike prices (X1 and X2) and 2 maturities (T1 and T2), one for each option. If X1 and X2 are 2 and 8 respectively, and T1 and T2 is 1 and 2 years respectively, calculate the value of the compound option with underlying asset of the second option the IBM stock with the data of 1a. Both options are European