Because an option grants the holder a right, it has value for the holder. It represents a liability for the issuer. Option valuation is any procedure for assigning a market value to an option. This is especially important when an option is issued, since the issuer will want to charge a reasonable price—what is called the premium—for the option.
whichever is greater.
Consider a call option on 200 ounces of gold struck at USD 375. If the market price of gold is USD 400 when the option expires, then the call's USD expiration value will be:
200 max( 0 , 400 – 375 ) = 5000.
This reflects the fact that the option holder can exercise the option to purchase 200 ounces of gold for USD 375 per ounce, and then immediately sell the 200 ounces at the market price of gold, which is USD 400 per ounce.
Suppose instead that the price of gold were USD 360 when the option expired. In this case, it would make no sense for the option holder to pay USD 375 for gold when the market price is only USD 360. The option holder would not exercise the option, and it would expire worthless. Its market value at expiration would be:
200 max( 0 , 360 – 375 ) = 0.
In the case of a put, its expiration value (per unit of notional amount) is either:
the difference between the strike price and the current value of the underlier,
whichever is greater.
Consider a put option on 200 ounces of gold struck at USD 400. If the market price of gold is USD 380 when the option expires, then the put's USD expiration value will be:
200 max( 0 , 400 – 380 ) = 4000.
This reflects the fact that the option holder can purchase gold at the market price of USD 380 and then exercise the put, selling the same gold for USD 400.
Option valuation is more complicated prior to an option's expiration. A useful notion is that of intrinsic value, which is simply what the option's value would be if the option were about to expire. Prior to expiration, an option's market value will generally exceed its intrinsic value by an amount that is called the option's time value.
For example, consider a call option on gold that is struck at USD 400 and will expire in three months. If the current price of gold is USD 390, is the option worthless? Would you be willing to give this option away for free? Certainly not! The option has no intrinsic value, but three months remain until it expires, and the price of gold may rise during that time. The option has time value.
An option is said to be at-the-money if the underlier value currently equals the strike price. Otherwise, the option is said to be in-the-money if it has positive intrinsic value, or out-of-the-money if it has zero intrinsic value. A call is in-the-money if the underlier value is above the strike price. A put is in-the-money if the underlier value is below the strike price.
While intrinsic value is easy to calculate, time value is more difficult to calculate. Historically, this made it difficult to value options prior to their expiration. Various option pricing methodologies were proposed, but the problem wasn't solved until the emergence of Black-Scholes theory in 1973.