Answer the following questions:

1. The current price of a non-dividend paying stock is $30. Use a two-step tree to value a European call option on the stock with a strike price of $30 that expires in 6 months. Each step is 3 months; the risk free rate is 5% per annum with continuous compounding. What is the option price when u = 1.15 and d = 0.85? Assume that the option is written on 100 shares of stock.

2. The current price of a non-dividend paying stock is $75. Use a two-step tree to value an American put option on the stock with a strike price of $72 that expires in 12 months. Each step is 6 months, the risk free rate is 5% per annum, and the volatility is 25%. What is the option price? Assume that the option is written on 100 shares of stock.