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No, intrinsic value can never be negative. It is positive when the option is in the money (ITM) and it is zero when the option is out of the money (OTM). It cannot be lower than zero.
The intrinsic value of an option contract is the value a trader would get if it were exercised today.
For call options, intrinsic value is calculated as-
Intrinsic Value = Spot Price - Strike Price
For put options, intrinsic value is calculated as-
Intrinsic Value = Strike Price - Spot Price
Now, let's understand why intrinsic value cannot be lower than zero.
It is because options contracts give traders a choice to exercise or not exercise the contract. A trader will only exercise the option or the choice when it is profitable to him. If he is in a loss he would allow the options to expire worthlessly and lose the premium paid for buying the option. He won't be losing any more money than the premium paid at the time of buying the contract.
Let's take an example to understand it better. Let's say you buy a call option of ABC stock with a strike price of Rs 200. You paid Rs 10 per share as the premium for the option. The ABC stock is currently trading at Rs 195, but you expect it to go up. It must go above Rs 200 to be profitable.
Now, say at the end of the month, it doesn't go up and is at Rs 196. Will any trader exercise it? No, because who would pay Rs 200 for a stock which is available at Rs 196? The trader will exercise his option or choice to not exercise the contract and will allow the option to expire worthlessly.
Yes, he will lose the premium of Rs 10 paid and so one can say that his trade is negative but the intrinsic value of the options never goes below zero.
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