Question 3 a) The current stock price is $15. Over each of the next two six-month periods, it is expected that the stock price will increase by 10% or decrease by 12%. The continuously compounded risk-free rate of interest is 5% per annum. i. What is the risk-neutral probability of an up state? wwwwww ii. What is the price for a one-year American put option with a strike price of $13.5? Please show the two-step binomial tree. iii. When should this one-year American put option be exercised? iv. Calculate delta at time 0. (15 Marks) b) Consider a position consisting of a $2,500 investment in asset A and a $3,000 investment in asset B. Suppose that daily volatilities of these two assets are 1.8% and 2.2%, respectively. The coefficient of correlation between their returns is 0.65. What is the 10-day 95% value at risk for the portfolio? What is the diversification benefit for the portfolio? (10 Marks) c) A European call option and put option on a stock both have a strike price of $12 and an expiration date in 3 months. Both sell for $2. The risk-free rate is 5% per annum. The current stock price is $11, and it pays a dividend of $0.5 one month later. Identify whether there is any arbitrage opportunity. (10 Marks) [Total marks: 35]