Suppose that a European call option to buy a share for ...

Suppose that a European call option to buy a share for $\$ 100.00$ costs $\$ 5.00$ and is held until maturity. Under what circumstances will the holder of the option make a profit? Under what circumstances will the option be exercised? Draw a diagram illustrating how the profit from a long position in the option depends on the stock price at maturity of the option.

Key Concepts

European_Call_Option

A European call option is a financial derivative that gives the holder the right, but not the obligation, to buy an underlying asset at a predetermined strike price only at the option's expiration. This type of option contrasts with American options, where the option can be exercised at any time up to and including the expiration date.

Option_Premium_and_Break-Even

The option premium is the price paid to purchase the option. The break-even point for a call option occurs when the underlying asset's price at maturity equals the sum of the strike price and the premium paid. The holder makes a profit only if the asset's price at maturity exceeds this break-even point, as the profit is the difference between the asset's price and this sum.

Option_Exercise_Condition

The decision to exercise a call option typically occurs when it is in-the-money, meaning that the underlying asset's price is above the strike price at maturity. Exercising the option enables the holder to buy the asset for less than its market value, making the action economically beneficial.

Profit_Payoff_Diagram

The profit payoff diagram for a long position in a call option is typically a kinked linear graph. For asset prices below the strike price, the option is not exercised and the loss equals the premium paid. For asset prices above the strike price, the profit increases linearly with the stock price, offset by the premium, illustrating that the holder's profit is the difference between the asset's price and the sum of the strike price and premium once the option is exercised.

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