A stock currently sells for $50. In six months, it will either rise to $55 or decline to $45. The risk-free interest rate is 6% per year.
1. Find the value of a European call option with an exercise price of $50.
2. Find the value of a European put option with an exercise price of $50, using the binomial approach.
3. Verify the put-call parity using the results of Questions 1 and 2.