The seller of an option gives away the good outcomes of the asset held by him to the option buyer for a price or premium.
How is this price or premium determined? The value of a call option at maturity is either zero or the difference between the price of the share (that is, the underlying asset) and exercise price. Thus,
Value of call option = Maximum share price – Exercise price
The option holder will exercise his option only when it is beneficial to do so. The call option will be beneficial to its buyer when the exercise price is less than the price of the share (the underlying asset). When the call option is out of the money (the exercise price is more than the price of the underlying asset), the minimum value of the call option at expiration will be zero.
How is the value of an option with time to expiration determined?
The value of an option depends on the following factors,
- Exercise price and the share (underlying asset) price
- Volatility of returns on the share
- Time to expiration
- Interest rates
Exercise price and value of underlying asset
Two important determinants of options are the value of the underlying asset and the exercise price. If the underlying asset were share, the value of a call option would increase as the share price increases. At the expiration date, the holder will know the share price, and he will exercise his option if the exercise price is lower than the share price. The excess of the share price over the exercise price is the value of the option at the expiration of the option. If the share price is more than the exercise price, a call option is said to be in the money. The deeper in the money is an option, the more is its value.
Volatility of underlying asset
How is the value of a call option affected by the volatility of the underlying asset? Let us consider an example.
Suppose you hold a two 2 months option on the share of Company Y. The exercise price is 100$ and the current market price is 100$. The option will be worthless if the share price remains 100$ at maturity. But prior to expiration, the option will be valuable if there are chances that the share price may rise above 100$.
Time to option expiration
The present value of the exercise price also depends on the time to expiration of the option. The present value of the exercise price will be less if time to expiration is longer and consequently, the value of the option will be higher. Further, the possibility of share price increasing with volatility increases if the time to expiration is longer. Longer is the time to expiration, higher is the possibility of the option to be more in the money.
Interest rates
The holder of a call option pays exercise price not when he buys the option, rather, later on, when he exercises his option. Thus, the present value of the exercise price will depend on the interest rate. The value of a call option will increase with the rising interest rate since the present value of the exercise price will fall. The effect is reversed in the case of a put option. The buyer of a put option receives the exercise price and therefore, as the interest rate increases, the value of the put option will decline.
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