The price, or premium, at which options trade is nor pre-set or determined by a formula, but is determined by open market forces. When the writer and the buyer of an option agree a price for a contract, then a trade can take place.
There are various factors market participants will consider in assessing the value of an options contract.
An options contract is said to be "in the money" if the current price of the underlying share is higher than the proposed exercise price of the option contract, assuming you are taking an option to buy the shares. This is also referred to as the option having "intrinsic value". Where an option has no intrinsic value it is said to be "out of the money".
This means that, for a call option: When the exercise price is lower than the current share price the option is in the money. When the exercise price equals the current price it is at the money and When the exercise price is higher than the current price the option is out of the money.
For a put option this is reversed. Where the exercise price is lower than the current price it is out of the money and when it is higher than the current price it is in the money.
This measures the value the option has because of the amount of time there is before it has to be exercised. It represents the premium an investor is prepared to pay for the chance that markets might move in their favor during the life of the option.
The longer the time to expiry, or the greater the market volatility is, the greater the time value of an option will be.
If a share is due to pay a dividend during the life of an option, it increases the premium that will be payable for a put option and decreases the premium on a call option. This is because; before the option is exercised the dividend will go to the potential seller of the shares, not the buyer. Another factor is movements in interest rates. An increase in interest rates will bring higher call option premiums and lower put option premiums. This reflects the projected cost of funding the purchase of the underlying shares. This cost is deferred by the buyer of an options contract, so the higher interest rates are , the more they will be asked to pay for the ability to defer those payments.
This is calculated using various mathematical formulae. For equity options the recognised industry standard for calculating fair value is the Cox Ross Rubenstein binomial model. This is calculated using estimates for; interest rates, volatility etc. and is , therefore, a subjective valuation. Actual trading levels often differ from fair value.