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 ST is the stock price in six months.

A) Use no-arbitrage arguments (you need to show how to set up the riskless portfolios at the different nodes of the binomial tree).

b) Use risk-neutral valuation.

c) Verify whether both approaches lead to the same result. [1 mark]

d) If the derivative is of American style (ST in the payoff function refers to the stock price when the option is exercised), should it be exercised early? [1 mark]