Problem $2(50$ points$)$

Problem 2 (50 points) The price of a share of Zoom stock is currently $250. It is known that at the end of 1 year, the Zoom share price will be either $312.50 or $200. The riskless interest rate is 2% per year. A. (10 points) Calculate the price of a I-year European call option on Zoom stock with an exercise price of $250 by applying the replicating portfolio approach. B. (10 points) Calculate the price of a I-year European call option on Zoom stock with an exercise price of $250 by applying the risk neutral valuation approach. C. (10 points) Calculate the price of a I-year European put option on Zoom stock with an exercise price of $250. D. (20 points) Next, add another I-year timestep; i.e., it is known that at the end of 2 years, the Zoom share price will be $390.63, $250, or $160. Calculate the price of a 2-year European call option on Zoom stock with an exercise price of $250. Also calculate the price of a 2-year European put option on Zoom stock with an exercise price of $250.