Currently, one share of ABC stock is valued at 92. You are given the following p
ID: 2750489 • Letter: C
Question
Currently, one share of ABC stock is valued at 92. You are given the following prices of European options on one share of this stock:
One-year 90-strike: Call= 11.65 Put =4.40
One-year 95-strike: Call= 8.30 Put =5.75
The force of interest is 6%. (FYI, the force of interest is often called the continuouslycompounded rate of interest.) (These problems ask you to calculate the profit or loss on the expiration date of the options. Thus, you will want to adjust any option premiums paid or received at the beginning of the life of the options, to their values at the end of the life of the options; this adjustment will reflect the time value of money.)
(1) You buy one 95-strike call option. On the expiration date of the option, ABC stock has a price of 101 per share. Find your profit or loss on the expiration date of the option.
(2) You buy one 90-strike put option. On the expiration date of the option, ABC stock has a price of 83 per share. Find your profit or loss on the expiration date of the option.
(3) You buy one 95-strike call option and sell one 90-strike put option. On the expiration date of the option, ABC stock has a price of 99 per share. Find your profit or loss on the expiration date of the option.
(4) You buy one 90-strike call option and you also buy one 90-strike put option. On the expiration date of the option, ABC stock has a price of 75 per share. Find your profit or loss on the expiration date of the option.
Explanation / Answer
1)
Normally Option sold on lots, therefore,One Option = 100 Share
Payoff at the end = Max{(Stock Price-Strike Price),0} * No of Share
Payoff at the end = Max{(101-95),0} * 100
Payoff at the end = $ 600
Call Premium = 8.30*100 = 830
Profit or loss on the expiration date of the option = Payoff at the end - Future value of Call Premium
Profit or loss on the expiration date of the option = 600 - 830*ert
Profit or loss on the expiration date of the option = 600 - 830 * 2.718281828459^(6%*1)
Profit or loss on the expiration date of the option = -281.32
2)
Normally Option sold on lots, therefore,One Option = 100 Share
Payoff at the end = Max{(Strike Price - Stock Price),0} * No of Share
Payoff at the end = Max{(90-83),0} * 100
Payoff at the end = $ 700
Put Premium = 4.40*100 = 440
Profit or loss on the expiration date of the option = Payoff at the end - Future value of Put Premium
Profit or loss on the expiration date of the option = 600 - 440*ert
Profit or loss on the expiration date of the option = 600 - 440 * 2.718281828459^(6%*1)
Profit or loss on the expiration date of the option = $ 132.79
3)
Normally Option sold on lots, therefore,One Option = 100 Share
Payoff at the end = Max{(Stock Price-Strike Price),0} * No of Share - Max{(Strike Price - Stock Price),0} * No of Share
Payoff at the end = Max{(99-95),0} * 100 - Max{(90-99),0} * 100
Payoff at the end = $ 400
Total Premium Paid = Call Premium Paid - Put Premium Recieved
Total Premium Paid = 8.30*100 - 4.4*100 =390
Profit or loss on the expiration date of the option = Payoff at the end - Future value of Total Premium Paid
Profit or loss on the expiration date of the option = 400 - 390*ert
Profit or loss on the expiration date of the option = 400 - 390 * 2.718281828459^(6%*1)
Profit or loss on the expiration date of the option = -14.12
4)
Normally Option sold on lots, therefore,One Option = 100 Share
Payoff at the end = Max{(Stock Price-Strike Price),0} * No of Share + Max{(Strike Price - Stock Price),0} * No of Share
Payoff at the end = Max{(75-90),0} * 100 - Max{(90-75),0} * 100
Payoff at the end = $ 1500
Total Premium Paid = Call Premium Paid - Put Premium Recieved
Total Premium Paid = 11.65*100 + 4.4*100 = 1605
Profit or loss on the expiration date of the option = Payoff at the end - Future value of Total Premium Paid
Profit or loss on the expiration date of the option = 1500 - 1605*ert
Profit or loss on the expiration date of the option = 1500 - 1605 * 2.718281828459^(6%*1)
Profit or loss on the expiration date of the option = -204.25
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