A stock index is currently 2,500. Its log-return volatility is 18% per annum. The risk-free rate is 8% per annum with continuously compounding and the dividend yield on the index is 2% per annum with continuous compounding. For convenience, lets assume that the value of index represents the dollar value. a) Calculate u, d, and p when a three-month time step is used. b) Lets use the values of u, d, and p calculated in a) and consider a two-step binomial tree model. What is the value of a six-month European put option written on the index with a strike price of 2,600. c) Lets use the values of u, d, and p calculated in a) and consider a two-step binomial tree model. What is the value of a six-month American put option written on the index with a strike price of 2,600.