The various factors which influence the option price are:

1. current price of the underlying asset.

2. strike price.

3. time to expiration of the option.

4. expected price volatility of the underlying asset over the life of the option.

5. short-term risk-free interest rate over the life of the option.

6. anticipated cash payments on the underlying asset over the life of the option.

The impact of each of these factors may depend on whether the option is a call or a put, and whether the option is an American option or a European option.

Current price of the underlying asset

Option price will change as the price of the underlying asset changes. For a call option, as the price of the underlying asset increases (all other factors being constant, and the strike price in particular), the option price increases. The opposite holds for a put option: as the price of the underlying asset increases, the price of a put option decreases.

Strike price

The strike price is fixed for the life of the option. All other factors being equal, the lower the strike price, the higher the price of a call option. For put options, the higher the strike price, the higher the price of a put option.

Time to expiration of the option

An option is a “wasting asset”. That is, after the expiration date the option has no value. All other factors being equal, the longer the time to expiration of the option, the greater the option price. This is because as the time to expiration decreases, less time remains for the underlying asset’s price to rise (for a call buyer) or fall (for a put buyer) – that is, to compensate the option buyer for any time premium paid – and therefore the probability of a favorable price movement decreases. Consequently, for American options, as the time remaining until expiration decreases, the option price approaches its intrinsic value.

Expected price volatility of the underlying asset over the life of the option

All other factors being equal, the greater the expected volatility (as measured) by the standard deviation or variance) of the price of the underlying asset, the more an investor would be willing to pay for the option, and the more an option writer would demand for it. This is because the greater the volatility, the greater the probability that the price of the underlying asset will move in favor of the option buyer at some time before expiration. Notice that it is the standard deviation or variance, not the systematic risk as measured by beta, that is relevant in the pricing of options.

Short-term risk-free interest rate over the life of the option

Buying the underlying asset ties up one’s money. Buying an option on the same quantity of the underlying asset makes the difference between the asset price and the option price available for investment at least) the risk-free rate. Consequently, all other factors being constant, the higher the short-term risk-free interest rate, the greater the cost of buying the underlying asset and carrying it to the expiration date of the call option. Hence, the higher the short-term risk-free interest rate, the more attractive the call option will be relative to the direct purchase of the underlying asset. As a result, the higher the short-term risk-free interest rate, the greater the price of a call option.

Anticipated cash payments on the underlying asset over the life of the option

Cash payments on the underlying asset tend to decrease the price of a call option because the cash payments make it more attractive to hold the underlying asset than to hold the option. For put options, cash payments on the underlying asset tend to increase their price.

Summary of actors that affect the price of an option: