Recall that options consist of a strike price and premium. The premium is determined by several factors like the price of underlying (security or index), time to expiry, volatility and risk-free interest rate.
Intrinsic value of an option: is defined as the amount by which an option is in-the-money, or the immediate exercise value of the option when the underlying position is marked-to-market.
For a call option: Intrinsic Value = Spot Price - Strike Price
For a put option: Intrinsic Value = Strike Price - Spot Price
The intrinsic value of an option must be positive or zero. It cannot be negative. For a call option, the strike price must be less than the price of the underlying asset for the call to have an intrinsic value greater than 0. For a put option, the strike price must be greater than the underlying asset price for it to have intrinsic value.
Price of underlying: The premium is affected by the price movements in the underlying instrument.
For Call options – the right to buy the underlying at a fixed strike price – as the underlying price rises so does its premium. As the underlying price falls so does the cost of the option premium.
For Put options – the right to sell the underlying at a fixed strike price – as the underlying price rises, the premium falls; as the underlying price falls the premium cost rises.
Time Value of an Option: Generally, the longer the time remaining until an option’s expiration, the higher its premium will be. This is because the longer an option’s lifetime, greater is the possibility that the underlying share price might move so as to make the option in-the-money. All other factors affecting an option’s price remaining the same, the time value portion of an option’s premium will decrease (or decay) with the passage of time.
Note: This time decay increases rapidly in the last several weeks of an option’s life. When an option expires in-the-money, it is generally worth only its intrinsic value.
Volatility: is the tendency of the underlying security’s market price to fluctuate either up or down. It reflects a price change’s magnitude; it does not imply a bias toward price movement in one direction or the other. Thus, it is a major factor in determining an option’s premium. The higher the volatility of the underlying stock, the higher the premium because there is a greater possibility that the option will move in-the-money. Generally, as the volatility of an under-lying stock increases, the premiums of both calls and puts overlying that stock increase, and vice versa.
Risk-free interest rate: this is not very important and can be ignored.