Minimum Value of a Call

In this section we formulate rules that enable us to better understand how call options are priced. It is important to keep in mind that our objective is to determine the price of a call option prior to its expiration day.

The minimum value of a Call

A call option is an instrument with limited liability. If the call holder sees that it is advantageous to exercise it, the call will be exercised. If exercising it will decrease the call holder's wealth, the holder will not exercise it. The option cannot have a negative value, because the holder cannot be forced to exercise it. Therefore:

                           C(S₀,T, X)≥ 0

For an American option, the statement that a call option has a minimum value of zero is dominated by a much stronger statement:

                        C_a(S₀, T, X))≥ Max(0, S_O - X)

The expression Max(0, S_O - X) means "Take the maximum of the two arguments, zero or S_O – X”.

The minimum value of an option is called its intrinsic value, sometimes referred to as parity value, parity, or exercise value.  Intrinsic value, which is positive for in-the-money calls and zero for out-of-the-money calls, is the value the call holder receives from exercising the option and the value the call writer gives up when the option is exercised. The intrinsic concept applies only to an American call, because a European call can be exercised only on expiration day. If the price of a European call were less than Max(0, , S_O - X), the inability to exercise it would prevent traders from engaging in the aforementioned arbitrage that would drive up the call's price.

The price of an American call usually exceeds its intrinsic value. The difference between the price and the intrinsic value is called the time value or speculative value of the call, which is defined as

C_a(S₀, T, X))- Max(0, S_O - X). The time value reflects what traders are willing to pay for the uncertainty of the underlying stock.

Intrinsic/Exercise/Parity Value

SO – X   if SO > X

0          if SO ≤  X