Question

A stock that does not pay dividend is trading at $20. A European call option with strike price of $15 and maturing in one year is trading at $6. An American call option with strike price of $15 and maturing in one year is trading at $8. You can borrow or lend money at any time at risk-free rate of 5% per annum with continuous compounding. Devise an arbitrage strategy.

Answer 1

For a stock which does not pay a dividend, there is no worth in exercising the American Call option before expiry.

Thus the value of both the options are the same

Now,

To gain profit from the difference in the price of American and European options. We will write an American Call option and earn a Premium of $8. Simultaneously we will buy a European Call option and pay $6 premium.

Hence, the net profit will be $2.

Since there is no worth in early exercise of American Option. Thus, both option will be exercised at maturity or may expire without exercising.

Hence, we will earn a profit of $2 for every American Call writing offset with a purchase of European Call