Problem:
Consider an option on a non-dividend-paying stock when the stock price is $30, the exercise price is $29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months.
Required:
Question 1: What is the price of the option if it is a European call?
Question 2: What is the price of the option if it is an American call?
Question 3: What is the price of the option if it is a European put?
Question 4: Verify that put-call parity holds.
Note: Please explain comprehensively and give step by step solution.