QUESTION FOUR a) A stock is currently trading at $50; its annual volatility is (0.40, the risk-free interest rate is 15% per annum with continuous compounding, and At is equal to three months. Use the binomial model to answer the following questions: i. Calculate the price of a 6-month European put option with an exercise price of $105 written on this stock. (5 marks) ii. Calculate the price of a 6-month American put option with an exercise price of $105 written on this stock. (5 marks) b) Answer the following questions: i. Explain in detail how volatility affects the values of call and put options. (10 marks) ii. Explain how one can measure the impact of changes in volatility on option prices. (5 marks) [TOTAL: 25 MARKS]