In this paper, you should use the relationship (1 + R) = 1 + i for rate conversion, where i is a given annual interest rate, mis number of periods in a year, and the corresponding period rate. 1. (75 marks) Consider a European call option on a stock for a strike price of $40 with expiration in 9 months. The initial stock price at i = 0 is $40. The stock price either increases by 1% or decreases by 1% after a period of 3 months. (One period is 3 months.) The risk-free interest rate is 2% per year throughout all periods considered in this question. In this question, your answers should contain at least 3 digits after the decimal point. (a) (15 marks) Use a binomial tree to show the stock prices for t = 0,1,2,3. Only the stock prices are necessary b) (15 marks) From time I = 0 to 1 = 1, the stock price increases by 1%, as stated above. Then, what is the percentage change in the price of the call option? (c) (15 marks) From time I = 0 to 1 = 1, the stock price decreases by 1%, as stated above, Then, what is the percentage change in the price of the call option? (d) (15 marks) Compute the replicating portfolio ho = (xoxo). le (15 marks) Show that Vivo), v(1) replicate the prices of the call option, In this paper, you should use the relationship (1 + R) = 1 + i for rate conversion, where i is a given annual interest rate, mis number of periods in a year, and the corresponding period rate. 1. (75 marks) Consider a European call option on a stock for a strike price of $40 with expiration in 9 months. The initial stock price at i = 0 is $40. The stock price either increases by 1% or decreases by 1% after a period of 3 months. (One period is 3 months.) The risk-free interest rate is 2% per year throughout all periods considered in this question. In this question, your answers should contain at least 3 digits after the decimal point. (a) (15 marks) Use a binomial tree to show the stock prices for t = 0,1,2,3. Only the stock prices are necessary b) (15 marks) From time I = 0 to 1 = 1, the stock price increases by 1%, as stated above. Then, what is the percentage change in the price of the call option? (c) (15 marks) From time I = 0 to 1 = 1, the stock price decreases by 1%, as stated above, Then, what is the percentage change in the price of the call option? (d) (15 marks) Compute the replicating portfolio ho = (xoxo). le (15 marks) Show that Vivo), v(1) replicate the prices of the call option