3. A non-dividend paying stock is currently trading at $5.24. Assume the continuously com- pounded annual interest rate is 5% and the annual volatility of the stock is 25%. (a) Determine the price of an American option written on the stock with the payoff function f(S) = S ln(S) 6.24 using a two-steps binomial tree model given the option matures in 6 months. (b) Determine the price of an European put option on the stock with exercise price of $5.65 maturing in 3 months using the Black-Scholes formula