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.

a. 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)

b. 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

c. 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

Buyer of call option has the right to buy the underlying at the agreed strike price at a specified time in future.

Payoff of Call option = Max(S_T-X,0)

Profit of Call option = Max(S_T-X,0) -C

Break even point = X+C

where S_T = Stock price at expiry T

X = Strike Price = $1625

C = call premium = $50.60

1.

2

Payoff = max(1550-1625,0)*100 = 0

Profit = payoff - premium = 0-50.60 = -50.60 loss

Payoff = max(1600-1625,0)*100 = 0

Profit = payoff - premium = 0-50.60 = -50.60 loss

Payoff = max(1675.60-1625,0)*100 = 5060

Profit = payoff - premium = 50.60-(50.60*100) = 0 profit/loss

3