Why an american call on a dividend pating stock is always worth at least as much as its intrinsec value ?

Question

and is the same true for european call ?

Answer 1

An American-style settlement call on a dividend paying company is always worth at least as much as the intrinsic value because you can immediately exercise the option.

For example, if a stock is trading at $50.00 per share, a call with a $40 strike price has an intrinisc value of $10. If the option could be purchased for $9 you could buy the option for $9 per share, immediately exercise it (paying at additional $40 per share to buy the stock) then sell the stock for $50 per share, giving you a risk-free profit of $1 per share.

Similarly, for a European-style settlement call on a stock that does not pay dividends the call will always be worth at least its intrinsic value unless the stock cannot be sold short. If the stock can be sold short, using the same dollar amounts as in the previous example, you could buy the call option for $9 per share, short the stock for $50 per share, giving you a net credit of $41 per share. At expiration you would exercise the option if the stock was still trading over $40 per share, once again giving you a risk free profit of $1 per share. (If the stock was below $40 per share you would simply cover the stock by purchasing it on the open market and letting the option expire, giving you a larger profit.)

However, for a European-style call on a stock that does pay a dividend, the price of the call may be less than the intrinsic value. For an example, use the same values as before but assume prior to expiration the stock will pay a $3 per share dividend. If you shorted the stock for $50 you would also have to pay an additional $3 per share for the dividend, reducing your total proceeds from the short stock position $47 instead of $50. Since your cost for the stock is $49 ($40 per share plus $9 per share for the option) you will lose $2 per share unless the stock drops below $40 per share at expiration, allowing you to cover your short stock position at a lower price.

Answer 2

It's intrinsic value is the value of the stock on the exchange. Regardless of whether or not you are collecting dividends, the stock is always worth AT LEAST it's intrinsic value, meaning what it can be sold for.