A stock price is currently $36. During each three-month period for the next six months it is expected to increase by 9% or decrease by 8%. The risk-free interest rate is 5%. Use a two-step tree to calculate the value of a derivative that pays off (max[(40-ST),0])2 where is the stock price in six months. a. What are the payoffs at the final nodes of the tree? [1 mark] b. Use no-arbitrage arguments (you need to show how to set up the riskless portfolios at the different nodes of the binomial tree). [2 mark] c. Use risk-neutral valuation.