A stock is currently traded at the price of $100. The price of the stock can go up or down by $20 next year. Assume investors are risk neutral and there are both European put and call options on the stock with an expiration date in one year. A student made the following three arguments.

1. If the interest rates are equal to zero then C(100) = P(100)
2. If the interest rates are higher than zero then C(100) > P(100)
3. Investors will never exercise both the put option and the call option

Which of the students arguments are correct?

a) Only I

b) Both I and II

c) Both I and III

d) All three arguments are correct

e) None of the arguments is correct