Consider binomial lattice with = 0.5, t = 1/365, interest rate of 1% per year. Use R to answer the following questions, assuming an exercise price of X = 100. (a) Calculate the price of call options with expiration T = 1 year for S0 ranging from 50 to 150 (b) Calculate the price of put options with expiration T = 1 year for S0 ranging from 50 to 150 (c) Verify that the put call parity holds (d) Consider a convertible ZCB with the following characteristics: the face value of the bond at the end of the year is 100, but you can choose to convert the bond into one share of the stock after six months. Assume that the stock price at time zero is S0 = 100. Use R to answer the following questions: i. In which scenarios for the stock price would you choose to exercise the option to convert in six month? ii. What is the value of the convertible ZCB in six month, just when you have the option to convert? iii. What is the value of the convertible ZCB at time zero? iv. What is the value of the option to convert at time zero?