Options are derivative securities. Because they derive their value from another asset, the price of that asset is often the factor that influences the option premium the most. For example, if a stock goes up in value, the call options on that stock will also appreciate in value while the puts depreciate.
If a stock goes down in value, the put options on that stock will appreciate, while the call options depreciate. An important aspect of this relationship is that it isn’t linear. For example, the underlying stock may move $1 and you may see the options premium rise by $.50. Then the underlying stock may move another $1, but the options premium only increases by $0.20. This non-linear relationship is a common theme in all aspects of option pricing.
Another important part of this correlation can be seen when considering the fact that options are leveraged instruments. Since options allow you to control a large amount of stock (specifically 100 shares per standard contract), naturally, the premium for options on a stock priced at $5 per share will be significantly less than the option premium for a stock priced at $500 per share. You are paying more for the option of a stock priced at $500 to control a more valuable underlying stock.
Options have an expiration date, and like anything that expires - time is a factor. The amount of time left until expiration is also known as the time value of an option. Options with long expiration dates have lots of time value, while options with short expiration dates have significantly less. This is because options with more time till expiration have more potential to become profitable, while the opposite is true for options with less time till expiration.
Market participants are willing to pay a higher premium for options with more probability of being profitable and less inclined to pay the lower the probability of profit goes. Time value is constantly decaying since expiration approaches every day. This is also known as “time decay”. Similar to the price of the underlying, how much an option decays is not constant. Time decay increases exponentially as expiration approaches. We will examine this concept more in detail when covering intrinsic vs extrinsic value.
Implied Volatility, also known as "IV," is the perceived move by investors that the underlying stock will have before expiration. Stocks that historically make big moves will have a higher IV, while stocks that historically make small moves will have a lower IV. High IV tends to lead to higher option premiums for both calls and puts while low IV tends to lead to lower options premiums for both calls and puts.
One of the deciding factors when pricing options is the IV. Not only does it allow you to approximate the future value of the option, but the current value of the underlying asset is also taken into consideration which is why not all option contracts are priced the same. For example, a smaller company with a lower share value will more than likely have a cheaper cost-per-contract versus a large company with a higher share value. It is important to note that options with high implied volatilities will have higher premiums and vise versa.