Today’s price of a non-dividend paying stock is $60. Use a two-step tree to value an American put option on the stock with a strike price of $50 that expires in 12 months. Each step is 6 months, the risk free rate is 10% per annum, and the volatility is 15%. Assume that the option is written on 100 shares of stock. a) What is the option price today? b) How would you hedge a position where you sell the put option today?