Question 5 (25 marks) A stock price is currently $31. It is known that at the end of 3 months it will be either $40 or $22. The risk-free rate of interest with continuous compounding is 4% per annum. (1) Calculate the value of a 3-month European at-the-money put option on the stock and verify that no-arbitrage arguments and risk-neutral valuation arguments give the same answers. (10 marks) (2) If the stock has a volatility of 20% per annum, by using a two-step binomial tree calculate the value of 6-month European and American put options with exercise price of $35. How does the delta of these two options change? (15 marks) Question 5 (25 marks) A stock price is currently $31. It is known that at the end of 3 months it will be either $40 or $22. The risk-free rate of interest with continuous compounding is 4% per annum. (1) Calculate the value of a 3-month European at-the-money put option on the stock and verify that no-arbitrage arguments and risk-neutral valuation arguments give the same answers. (10 marks) (2) If the stock has a volatility of 20% per annum, by using a two-step binomial tree calculate the value of 6-month European and American put options with exercise price of $35. How does the delta of these two options change? (15 marks)