Option Pricing

1. Intrinsic value
2. Time value

1. Intrinsic Value
   
   An option’s premium at any given time is the total of its intrinsic value and its time value. The total premium is the only number you will see or hear quoted. However, it is important to understand the factors that affect time value and intrinsic value, as well as their relative impact on the total premium.
   
   Intrinsic value + Time value = Premium
   
   Intrinsic Value—This is the amount of money that could be currently realized by exercising an option with a given strike price. An option’s intrinsic value is determined by the relationship of the option strike price to the underlying futures price. An option has intrinsic value if it is currently profitable to exercise the option. A call option has intrinsic value if its strike price is below the futures price. For example, if a soybean call option has a strike price of $6.00 and the underlying futures price is $6.50, the call option will have an intrinsic value of 50 cents. A put option has intrinsic value if its strike price is above the futures price. For example, if a corn put option has a strike price of $2.60 and the underlying futures price is $2.30, the put option will have an intrinsic value of 30 cents.
   
   Determining Intrinsic Value
   Calls: Strike price < Underlying futures price
   Puts: Strike price > Underlying futures price
   
   Option Classification
   At any point in the life of an option, puts and calls are classified based on their intrinsic value. The same option can be classified differently throughout the life of the option.
   
   In-the-Money—In trading jargon, an option, whether a call or a put, that has intrinsic value (i.e., currently worthwhile to exercise) is said to be in-the-money by the amount of its intrinsic value. At expiration, the value of a given option will be whatever amount, if any, that the option is in-the money. A call option is in-the-money when the strike price is below the underlying futures price. A put option is in-the-money when the strike price is greater than the underlying futures price.
   
   Out-of-the-Money—A call option is said to be out-of-the-money if the option strike price is currently above the underlying futures price. A put option is out-of-the-money if the strike price is below the underlying futures price. Out-of-the money options do not have any intrinsic value.
   
   At-the-Money—If a call or put option strike price and the underlying futures price are the same, or approximately the same, the option is at-the-money. At-the-money options do not have any intrinsic value. To repeat, an option’s value at expiration will be equal to its intrinsic value—the amount by which it is in-the-money. This is true for both puts and calls.
   
   Determining Option Classifications
   
   In-the-money
   Call option: Futures price > Strike price
   Put option: Futures price < Strike price
   
   Out-of-the-money
   Call option: Futures price < Strike price
   Put option: Futures price > Strike price
   
   At-the-money
   Call option: Futures price = Strike price
   Put option: Futures price = Strike price
   
   Calculating an Option’s Intrinsic Value
   Mathematically speaking, it is relatively easy to calculate an option’s intrinsic value at any point in the life of an option. The math function is basic subtraction. The two factors involved in the calculation are the option’s strike price and the current underlying futures price.
   
   For call options, intrinsic value is calculated by subtracting the call strike price from the underlying futures price.
   
   
   • If the difference is a positive number (i.e., the call strike price is less than the underlying futures price), there is intrinsic value.
   • Example: 22 December soybean oil call when December soybean oil futures is trading at 23 cents. (23 cents – 22 cent strike price = 1 cent of intrinsic value)
   • If the difference is 0 (i.e., call strike price is equal to the underlying futures price), then that call option doesn’t have any intrinsic value.
   • Example: 22 December soybean oil call when December soybean oil futures is trading at 22 cents. (22 cents – 22 cent strike price = 0 intrinsic value)
   • If the difference is a negative number (i.e., call strike price is greater than the underlying futures price), then the call option currently doesn’t have any intrinsic value.
   • Example: 22 December soybean oil call when December soybean oil futures is trading at 20 cents. (20 cents – 22 cent strike price = 0 intrinsic value)
   
   
   Note. Intrinsic value can only be a positive number (i.e., an option can’t have negative intrinsic value). Therefore, you can say the call option in this example is out-of-the-money by 2 cents but you shouldn’t say that it has a negative 2 cents intrinsic value.
   
   For put options, intrinsic value is calculated by subtracting the underlying futures price from the put strike price.
   
   
   • If the difference is a positive number (i.e., the put strike price is greater than the underlying futures price), there is intrinsic value.
   • Example: $3.50 March wheat put when March wheat futures is trading at $3.20. ($3.50 strike price – $3.20) = 30 cents of intrinsic value)
   • If the difference is 0 (i.e., put strike price is equal to the underlying futures price), then that put option doesn’t have any intrinsic value.
   • Example: $3.50 March wheat put when March wheat futures is trading at $3.50. ($3.50 strike price - $3.50 = 0 intrinsic value)
   • If the difference is a negative number (i.e., put strike price is less than the underlying futures price), then the put option currently doesn’t have any intrinsic value.
   • Example: $3.50 March wheat put when March wheat futures is trading at $3.75. ($3.50 strike price - $3.75 = 0 intrinsic value)
   
   
   Note. Intrinsic value can only be a positive number (i.e., an option can’t have negative intrinsic value). Therefore, you can say the put option in this example is out-of-the-money by 25, but you shouldn’t say that it has a negative 25 cents intrinsic value.
   
   At the expiration of a call or put option, the option’s premium consists entirely of intrinsic value—the amount that it is in-the-money.
   
   



2. Time Value
   
   If an option doesn’t have intrinsic value (either it’s at-the-money or out-of-the-money), that option’s premium would be all time value. Time value is the difference between the total premium and the intrinsic value. Total premium - Intrinsic Value = Time value Although the mathematics of calculating time value is relatively easy when you know the total premium and the intrinsic value, it is not quite as easy to understand the factors that affect time value.