In contrast, European options can be exercised only on the maturity date. Since American options provide the owner an additional timing option (to exercise early), they cannot be less valuable than equivalent European options. Given the fact that European options are easier to analyse than American options, and properties of an American option are frequently deduced from those of its European counterpart, our discussion in this Chapter primarily focuses on European options.
The call option buyers expect the price of securities to go up as it benefits them. They are bullish. The reverse holds true for the call writers, they expect/hope the price of securities to fall. They are bearish. In case of the decrease in price, the call buyer does not buy the securities (as the prevailing share price is less than the exercise price).) In such a situation, the call writer gains equivalent to the option premium he has received at the time of selling the call option:
From the above discussion, it can be deduced that the value of call option is either zero (when the prevailing share price, S1 on the date of maturity is equal to or less than the exercise price, E) or positive (when S1 > E>. It cannot be negative as it implies that the call-holder buys the share at E price which is higher than the market price of the share, S1. Obviously, no rational investor will act that way. The value of call option (C1) on is expiration date is given by Equation 5.1
C1 = Max (S1-E, 0)
Where Max implies the maximum value of S1 - E or Zero whichever is higher.