7. (10 points) A stock price is currently at $50 and has a volatility of 30% p.a. The risk-free interest rate is 1% p.a. with continuous compounding. (a) Use a three-step binomial tree model with step size 3 months to compute the arbitragefree price of an American put option written on that stock with strike price of $50 and maturity in 9 months. (b) At which nodes in the tree would it be optimal for the holder to early exercise the American put option before maturity T ? 7. (10 points) A stock price is currently at $50 and has a volatility of 30% p.a. The risk-free interest rate is 1% p.a. with continuous compounding. (a) Use a three-step binomial tree model with step size 3 months to compute the arbitragefree price of an American put option written on that stock with strike price of $50 and maturity in 9 months. (b) At which nodes in the tree would it be optimal for the holder to early exercise the American put option before maturity T