X Communicated to Y That He Was Selling His House

X communicated to Y that he was selling his house and lot and gave him an option to buy the same up to the end of the month of September. Y accepted the offer with an agreement that Y will allow X to stay in his house in Los Angeles, California during Christmas time that year. Is the option binding upon X?

A) The option is not binding since no payment in the form of money was delivered to X by Y.
B) The option is not binding because no property or anything of value was delivered to X by Y.
C) The option is binding as the consideration can be in an undertaking.
D) The option is not binding or void because no consideration at all was paid.