4. (a) Suppose that we have a 6-month European call option with K = 23. The stock is currently priced at 22 and in two time steps of three months it can go up or down by 10%. The annual risk free interest rate is 12%. i. Compute the value of the call option today. (8 marks) ii. Hence, or otherwise, find the current value of the corresponding put option. (2 mark) iii. State the European option pricing formula for the case of the n-period Binomial model and explain how you would use the result to estimate the current value of a 5 year (n = 20) option (you do not have to give an actual estimate). (3 marks) (b) For a two period binomial model you are given: i. Each period is one year. ii. The current price of the stock is 20. iii. u= 1.2840 and d=0.8607 iv. The continuously compounded risk free annual interest rate is 5%. Calculate the price of an American call option on the stock with a strike price of 22. (7 marks) 4. (a) Suppose that we have a 6-month European call option with K = 23. The stock is currently priced at 22 and in two time steps of three months it can go up or down by 10%. The annual risk free interest rate is 12%. i. Compute the value of the call option today. (8 marks) ii. Hence, or otherwise, find the current value of the corresponding put option. (2 mark) iii. State the European option pricing formula for the case of the n-period Binomial model and explain how you would use the result to estimate the current value of a 5 year (n = 20) option (you do not have to give an actual estimate). (3 marks) (b) For a two period binomial model you are given: i. Each period is one year. ii. The current price of the stock is 20. iii. u= 1.2840 and d=0.8607 iv. The continuously compounded risk free annual interest rate is 5%. Calculate the price of an American call option on the stock with a strike price of 22. (7 marks)