Question

Apple stock is trading at 489.64 today. If Apple stock call option expiring in 7 days at strike 300.0 is trading at $100, what opportunities are there for an arbitrageur? (hint: check the lower boundary of a call’s price, S0-Kexp (-rT), and see that the call price is too low, therefore there is arbitrage.)

Answer 1

Current trading price = 489.64

Call option with maturity after 7 days have strike price of 300.

Call option premium = $100.

For an arbitrageur the following Opportunities are available-

• Buy a call option today for getting the right to buy the Apple stock after 7 days at a price $300 and pay option premium of $100 by borrowing at risk free rate
• After 7 days buy the apple stock as per the call option by paying $300.
• Total cost is $300+$100+Interest on borrowing
• Assuming the price of Apple stock has not changed much, then sell the Apple stock at market rate at higher rice and obtain the arbitrage gain
• Arbitrage gain = Amount received by selling apple stock - $300-$100-Interest on borrowing.