Question 3 (7 marks) A European derivative instrument on IBM has the following payoff structure at the maturity date in 3 years: a) ST if ST < 120 b) 120 + 2 * (ST 120) if 120 < = ST <= 160 c) 200 if 160 <= ST <= 200 d) ST if 200 <= ST where ST is the price at the maturity date. The spot price is 154 and the volatility is 25%. The risk-free interest rate is 4% and we consider a 6-step binomial tree. (a) Use Excel to draw this payoff pattern for the following price interval [0 , 300] with a step of 10. (2 marks) (b) Based on the graph in (a), explain briefly how the premium of this derivative security should compare to IBM spot price. (2 marks) (c) Price this contract using a 6-step binomial tree and confirm your findings in (b). Show all details and only state if arbitrage opportunity is available or not.