Short answer: No. Intrinsic value of an option can’t be negative.
It is positive for in the money options. It is zero for out of the money options. It can’t be lower than zero, due to the very nature of options – the option (choice) to act (exercise) only when it’s profitable to you.
Let’s see in more detail how intrinsic value is calculated for calls and puts, and why it can’t be negative.
Intrinsic value of an option is the value one would gain from exercising the option immediately. Generally, it is the positive difference between the option’s strike price and the current market price of the underlying security. It is different for calls and puts.
For call options, which represent rights to buy the underlying security at a given price (strike price), intrinsic value is equal to the higher of:
For put options, which represent rights to sell the underlying at strike price, intrinsic value is the higher of:
When owning an option, what is the worst case scenario?
It is that you hold the option until expiration and it expires worthless, making you lose the entire initial investment (the option premium paid). Once you have paid for buying an option, you can’t lose more than that.
For example, let’s say you buy a call option on Bank of America (BAC) stock with strike price of $20 expiring in one month. Let’s say you have paid $1.15 per share for the option (the premium), which is your maximum possible loss from the trade, but for our purpose it is not really important, because initial cost does not affect intrinsic value calculation in any way.
The stock is currently trading at $19.50, but you believe it will go up. It must go above $20 for the option’s exercise to be profitable.
Unfortunately, you are wrong and the stock ends up at $19.20 just before the option expires. Will you exercise the option?
Of course not, because exercising the $20 strike call option would mean buying the BAC stock for $20 per share, while it is worth only $19.20 in the stock market. You would lose $0.80 by exercising the option. Does this mean the option’s intrinsic value is negative $0.80?
Fortunately, options give you the right, but not the obligation to exercise. Generally, you will only choose to exercise when doing so would be profitable for you. In our example, exercising the option would lead to a loss of $0.80 per share ($80 for one option contract of 100 shares). Therefore you choose to not exercise the option and just let it expire.
An option always gives you two alternatives: to exercise or not to exercise.
It makes sense to always choose the better of the two outcomes, which is never worse than zero.
The option’s intrinsic value, which is the value of the possibility to exercise the option, is always equal to the better outcome. Therefore it can’t be lower than zero.