A stock is expected to increase or decrease by 20% every 6 months over the next year. The current stock price is $50. The 6-month riskfree rate is 10% (semi-annually compounded).

(15 pts) What is the price of an at-the-money European put (ie. strike price= current stock price) with a maturity of one year?

(15 pts) What is the price of an at-the-money American put with a maturity of one year? What is the exercise policy for this American put? Be specific of whether and when early exercising the option is optimal