Option premium consists of intrinsic value, which is either zero or positive, plus time value. Intrinsic value cannot be negative because the holder is never obliged to exercise a contract that is out-of-the-money. Even if an option has zero intrinsic value it will still have some time value, assuming that it has not yet expired and the price of the underlying can fluctuate to any extent. The time value reflects the chance or possibility that the option may become in-the-money before expiration. Generally speaking, this chance is greater:
the longer the time remaining until the expiry of the option;
the greater the volatility of the price of the underlying asset.
Taken together these factors – time to expiry and volatility – represent opportunities for the buyer of an option and risks for the seller or writer of the contract. Time value is the price of that opportunity and that risk. Calculating intrinsic value is easy, but it is more difficult to calculate time value. The problem is that unlike (say) a US Treasury bill, the future cash flow arising from an option is inherently uncertain and depends on what happens to the price of the underlying over the life of the contract. To value an option we need a pricing methodology that is based on probability – taking into account the possible future cash flows that might result from buying or selling an option, and the probabilities that those will occur. This is the conception that underlies ...