1. A stock is currently trading at $100; its annual volatility is 0.28, and the risk-free interest rate is 12% per annum with continuous compounding. Answer the questions below using a two-step binomial model where ∆t is equal to three months (show all the details of your calculations and display the results with four decimal places):

1. Calculate the values of u, d, and p.

2. Calculate the price of a 6-month European put option with an exercise price of $105 written on this stock.

3. Calculate the price of a 6-month American put option with an exercise price of $105 written on this stock.