Math 2016 – TAMU DM – Call and Put Options
Call Options
1. Chris buys a one-year 50-strike European call option from Kevin for a premium of $7.43. The
risk-free interest rate is 6.5% effective. For what spot price at expiration is Wayne's profit 0?
2. Ben buys a 80-strike European call on Asset A and sells a 70-strike European call on Asset B. The
spot price at expiration of both assets is S. Ben's total payoff under the two options is –3. Determine
S.
1

Math 2016 – TAMU DM – Call and Put Options
3. Tim buys a one-year 125-strike European call for a premium of $16.86. He sells a 100-strike call on
the same underlying asset for a premium of $31.93. The spot price at expiration is $110. The
effective annual interest rate is 3.5%. What is Tim's total profit at expiration for the two options?
4. Todd believes that the price of oil, currently at $60 per barrel. Will increase in the next year. He
purchases a 12-month European call option on 1,000 barrels of oil, with an exercise price of $65 per
barrel, for $2000. At the time of expiration of option, the market price of oil is $63.25 per barrel. The
annual continuously compounded rate is 6.5%. Find the profit or loss, at maturity of the option, on
Todd's investment.
5. Suppose Mandi believes that the oil price, currently at $55 a barrel, will increase slightly but not
significantly, in the next year. She makes the following transactions:
• Buy a 12-month call option, with an exercise price of $55 a barrel, on 1,000 barrels of oil.
• Sell a 12-month call option, with an exercise price of $60 a barrel, on 1,000 barrels of oil.
The price of oil at the time of expiration on the two options is X per barrel. The payoff for Mandi's
combined position is 1,290. Find X .
2

Math 2016 – TAMU DM – Call and Put Options
Put Options
1. Patrick buys a 6-month 65-strike European put with a premium of $4.53. He also writes a 6-month
75-strike European put with a premium of $10.56 on the same underlying asset. The annual risk-free
interest rate is 6% effective. The spot price at expiration is $68. patrick's total profit on the two
options is X . Determine X .
2. Cameron writes a one-year 110-strike European out with a premium of $10.93. The risk-free interest
rate is 3.85% per year. What is the range of Cameron's profit from minimum to maximum?
3

Math 2016 – TAMU DM – Call and Put Options
3. You own a share of ABC corp. stock which is currently priced at $104. You decide to invest in a long
3-month put with a strike price of $100 on that share, which you purchase for $1.75. The annual
continuously compounded rate of interest is 10%. What is the maximum possible profit, evaluated at
expiration of the put, on your put investment?
4. A fire insurance policy covers a house worth $300,000. The policy ahs a deductible of $1,000 and a
premium of $500 The insured payoff on the policy is expressed in the form of a purchased put.
Determine the strike price, X.
4

Math 2016 – TAMU DM – Call and Put Options
5. Tim buys a 6-month 100-strike European call with a premium of $9.98. Rob writes a 6-month
90-strike European put with a premium of $3.08 on the same underlying asset. The risk-free interest
rate is 6.5% compounded semiannually. For what range of spot prices at expiration is rob's profit
greater than Tim's?
5