Question

Suppose a European call option to buy a share for $22.50 costs $1.75. The stock currently trades for $20.00. If the option is held to maturity under what conditions does the holder of the option, make a profit? Note: ignore time value of money. How would the answer change if this was an American call option?

Answer 1

The major difference between the American option and European option is timing of exercising the option.European option can be exercised only at the time of maturity date whereas the American option can be exercised at any time before the maturity date.

The holder of the call option is benefited only if the price raises more than Dollar 22.5

For ex: If the price in the market raises to 23.5 Dollies then

Gain on the contract.( $ 23.5-$22.5). = $ 1

Less: premium paid. = $ 1.75

Net loss on the contrat = $ 0.75,

So, in order to gain from the contrat, the share price should raise to more than $ 24.25($ 22.5+$ 1.75).so if the share price is more than $ 24.25 then the holder is benefited from the contract.

Eg: Share price raises to $ 25

Gain on option contract($ 25-$ 22.5) = $ 2.5

Less: call premium. = $ 1.75

Profit from the option contract. = $ 0.75

Note: If the price falls below $ 22.5 then the option will lapse.

In case of American call option , we have to exercise the option,when the share price reaches above exercise price to get a profit The option should be exercised before the maturity date.