In Defining Stock Options and Distinguishing Between the Two Types of Stock Option Contracts,  as a stock option holder, you are under no obligation either to buy the underlying shares as a call holder or to sell the underlying shares as a put holder.

There are three things that will happen.

1. If you do elect to buy or sell the underlying shares of stock, that is known as exercising an option.
2. You may also elect to sell your option on the open market.
3. Your option may expire. If you choose neither to exercise your option nor to resell it, it may expire. But when an option expires, it loses all of its value.

All options have expiration dates, and we will elaborate further on that topic in Realizing That Stock Options Expire.