A financial institution offers a derivative security called PutSQ with a payoff equal to max (580 - [ST]2, 0) at maturity, where STis the stock price at maturity in 1 year and [ST]2is its square. Assume that the current stock price is $20 and that no dividend will be paid. The stock volatility is 30% and the risk-free interest rate is 2.40%.

Use a 4-step binomial tree to compute the price of this derivative assuming it is American-style, i.e. it can be exercised at any time during its life.Show all details andexplain clearly your steps.