Hey Hai Tao,
My CFA textbook had a conclusion I don't believe.
Say there is a microsoft stock call option expiring 7/1/2011, X = $20, in-the-money, American style
Say there is an identical microsoft call but European style.
Assumption: the underlying stock makes no dividend or other cash payment before expiration.
Under this assumption, textbook says both call options are worth the same.
Earlier the same author said that an American option is worth at least the same as an European style option, but under this Assumption, he claims they have equal valuation.
As a Layman, my intuition tells me the American option is more valuable. Suppose my analysis tells me Microsoft might drop to $19, then the American option lets me pay $2000 today for 100 shares and sell today at $2467, earning a profit of $467. The European option may expire out of the money and worthless.
Do you agree?