An option is a claim without liability. It is a claim contingent upon the occurrence of certain conditions. Thus, an option is a contingent claim. More specifically, an option is a contract that gives the holder (buyer) a right, without any obligation, to buy or sell an asset at an agreed price on or before a specified period of time. The option to buy an asset is known as a call option, and the option to sell an asset is called a put option.
A call option is exercised when:
Share price at expiration (S) is greater than Exercises price (E)
That is, S > E
In another way, it can be said that the value of a call option (C) at expiration is:
Maximum [(Share Price – Exercise Price),0]
C = Max(S-E,0)
The above expression means that the value of a call option at expiration is the maximum of the share price minus exercise price or zero. This means that the value can never be negative.
For example, the value of a call option and a put option can be determined from the following table:
If Shape Price is S, Exercise Price is E and Value of Call Option is C, for a call option, the value will be:
For a put option, it will be exercised when E > S
The value of put option at expiration will be:
where P = value of put
Applying this principle, the value of put option from the example above will be:
From the analysis above:
Value of call = (-1) * Value of put