Question

You are bullish on Amazon’s stock (AMZN) which is currently selling for $1596.50. You have decided to buy a 6-month call option with a strike price of $1,625. It costs $50.60 per share to buy the option. Assume the 6-month risk-free rate is 1% per annum with continuous compounding.

1. Draw the profit and payoff function for the long call option at expiration? (Provide labels for the axes and label a point on the functions above, below and at the strike)

2. Note each contract is for 100 call options. Calculate what the payoff and profit at

   expiration is if the spot price is _______. i. $1,550

   ii. $1,600 iii. $1,675.60

3. Draw the profit and payoff function for the short call option at expiration? (Provide labels for the axes and label a point on the functions above, below and at the strike)

Answer 1

Call option gives option buyer the right to buy the Stock at a strike price at a specified time in future.
Profit of Call option buyer is given by following equation:
Payoff of Call option = Max(ST-X,0)
Profit of Call option = Max(ST-X,0) -c
where ST is stock price at maturity, X is exercise price and c is premium paid to buy the Call option.
Profit of Call option seller is given by following equation:
Payoff of Call option seller = -Max(ST-X,0)
Profit of Call option seller = -(Max(ST-X,0) -c)
where ST is stock price at maturity, X is exercise price and c is premium paid to buy the Call option.