The market determines the premium of an option through supply and demand. However, much research has been done on options pricing, most importantly, the Black-Scholes model. In essence, these models explain that in a risk-neutral world, we can determine a fair market value for options. At this fair market value, the option premium is in equilibrium with the expected discounted return of that option.
There are two components to option prices:
- The intrinsic value is the amount, by which the option is in the money. Therefore, the intrinsic value is always greater than or equal to zero. On expiration day, the intrinsic value becomes the amount the holder of the option receives, and the writer of the option owes.
- The extrinsic or time value is the remainder after we subtracted the intrinsic value. This value reflects the probability of reaching or exceeding the strike price by expiration. The time value decays and becomes zero on the expiration day.
Options on stocks and ETFs are physically settled, meaning that the underlying changes hands, when the option is executed. Index options cannot be settled physically, and are therefore settled in cash instead: the option holder receives the amount by which the option is in the money from the option writer.