Exercising a call option that is under water would cause the option holder to pay a price for shares higher than the current market price. Similarly, exercising a put option that is under water would cause the option holder to dispose of shares at price lower than the current market price.
Despite this, options have that are under water have value. In the case of call options, there is a possibility that, in the time before expiration date, the stock price will rise so that the call options are in the money. Likewise, in the case of put options, there is a possibility that the stock price will fall so that the put options are in the money.
The Black-Scholes value approximates the fair value of a tradable call option, even one that is under water. The main function of these pages is to calculate and interpret the current Black-Scholes value of a call option with a given strike and time to expiration.