The premium is determined by market forces but there are more factors affecting the market view of the option premium than is the case with prices of the underlying stocks. These factors include:
Underlying stock price - The underlying stock price is normally the most significant factor affecting the price of an option. In-the-money options enable holders to buy or sell the underlying stock at a better price than the prevailing securities market price. They therefore cost more than the equivalent at-the-money and out-of-the-money options because there is more value in them. And whether an option is in-the-money depends solely on the underlying stock’s price because the option’s strike price is fixed. The difference between the strike price of an in-the-money option and the price of the underlying stock is called the intrinsic value. For example, a call option with a strike price of $45 when the underlying stock’s price is $50 has an intrinsic value of $5. However, it is possible that the call option in this case will be traded above $5. Even out-of-the-money and at-the-money options, which have no intrinsic value, will normally have some value in the market. This is because there are other factors determining the value of the option. These are called “extrinsic” factors (or sometimes "time value" factors). The extrinsic factors are time until expiration, dividend expectation, interest rate and volatility.
Time Until Expiration - All other things being equal, the value of an option will diminish as the option approaches expiry, and the rate at which it diminishes will be faster the closer it gets to expiry so that close-to-expiry, out-of-the-money options can lose their value very quickly. It is for this reason that an option is often referred to as a “wasting asset”.
Dividend - The dividend factor generally only applies to stock options because most other underlying assets do not pay dividends. All other things being equal, a cash dividend will lower the share price by the present value of the dividend on the day the stock first trades “ex-dividend”. The larger the dividend, the more the stock price is expected to fall. This change in the stock price in turn affects the option premium.
A higher dividend results in a drop in the premium for the call but a higher premium for the put.
Interest rate - A rise in interest rates will raise the value of call options, and lower the value of put options. Interest rates may be regarded as an opportunity cost. Since an option is a leveraged instrument, a call option holder does not need to pay the full value of the underlying stock, and can invest remaining funds in interest-bearing instruments.
Volatility - Risk is the probability that the price of the underlying stock will move, within the life of the option, from its present value to a point where the option writer incurs losses. The greater the probability that this will happen, the greater the risk and hence the higher the premium, whether call or put.
The degree of expected fluctuation in the underlying stock price determines the extent of the risk. The measure of this fluctuation is most commonly referred to as “volatility”. Implicit in any option premium are assumptions about the likely volatility of the stock. For this reason, one generally speaks of the “implied volatility” of the option premium, ie the likely volatility of the underlying stock is “implied” by the option premium. Expressed as a percentage, volatility is closely monitored by option market users as a vital indicator.
The impacts of the above factors on option premium are summarised below: