Problem:
A stock price is currently $30. Every 6 months the price will either go up by 12% or down by 8%. The risk-free rate is 4% per annum with continuous compounding.
Required:
Question 1: Compute the price of a one-year European put option with strike price $32.
Question 2: Compute the price of a one-year American put option with strike price $32.
Note: Please show guided help with steps and answer.