MATH 373

Spring 2013

Test 4 May 2, 2013

1. (2 points) List the four uses of derivatives.

2. (6 points) Malcolm buys 100 shares of the stock of Jiang Corporation at the same time that

Ningzhu sells 100 shares of the stock of Jiang Corporation.

The commission on Malcolm’s purchase is 0.50 per share while the commission on Ningzhu’s

sale is 1% of the total price.

Malcolm pays 4150 including commissions to purchase his 100 shares.

The total transaction costs incurred by both Malcolm and Ningzhu are 130.60

Calculate the Bid Price for one share of Jiang Corporation.

3. (5 points) Alicia buys an 8 month European style 30 strike put option on the stock of Losby LTD.

The premium for the put is 2.20.

The current spot price of Losby LTD stock is 29.50.

The annual effective risk free interest is 5%.

Determine the payoff and profit on this put if the spot price of Losby stock at the end of 8

months is 29.75.

4. (4 points) The S&P 500 Index pays dividends at a continuous annual rate of 2.5%.

The annual risk free interest rate compounded continuously is 2%.

The 2 year prepaid forward price on the S&P 500 index is 1600.

Determine the current spot price of the S&P 500 Index.

5. (5 points) The current spot price of the stock of Walker LTD is 62. Walker stock does not pay a

dividend.

The forward price on a 2 year forward contract on Walker LTD is 65.

The annual effective risk free interest rate is 3%.

Assuming that there are no transaction costs, state what actions and positions you would take

today (time 0) to take advantage of this arbitrage opportunity.

6. (3 points) Circle each of the following that are true with regard to a Bull Spread. You can

circle 0, 1, 2, or all 3 items.

You can create a Bull Spread by buying a call with a low strike price and selling a call with a high

strike price.

You can create a Bull Spread by buying a put with a high strike price and selling a put with a low

strike price.

The following is the graph of a Bull Spread.

7. (1 point) The payoff on the sale of a zero coupon bond is always zero.

True False

8. (1 point) The future value of the cost of a long forward contract is always zero.

True False

9. (6 points) Glick Gold Exporters has entered into a swap where Glick will purchase 10,000 ounces

of gold at the end of one year, 20,000 ounces of gold at the end of 2 years, and 25,000 ounces of

gold at the end of 3 years.

You are given the following information:

Time t Spot Interest Rate Forward Price of Gold at Time t

1 0.030 1400

2 0.033 1450

3 0.037 1510

4 0.042 1550

5 0.048 1575

Calculate the swap price the Glick will pay under this swap.

10. (8 points) Man Industries has a line of credit of 1,000,000. Under this line of credit, Man can

borrow 1,000,000 at a floating interest rate that changes each year. Man enters into a swap in

order to fix the interest rate that must be paid on this line of credit over the next 3 years.

You are given the following information:

Time t Spot Interest Rate

1 0.030

2 0.033

3 0.037

4 0.042

5 0.048

Calculate the fixed interest rate that Man will pay under the swap.

11. (5 points) On May 2, 2010, Beckley Farms entered into a swap agreement. With this swap,

Beckley Farms agreed to buy 100 tons of fertilizer at the end of each year for the next five years.

The swap price under this agreement was 500 per ton.

On May 2, 2013, Beckley Farms decides to sell the swap which now has two years left.

On May 2, 2013, the follow are the spot interest rates and forward prices for fertilizer:

Time t Spot Interest Rate Forward Price of One Ton of

Fertilizer at Time t

1 0.030 490

2 0.033 525

3 0.037 540

4 0.042 560

5 0.048 570

Determine the market price of this fertilizer swap.

12. (1 point) Which of the following is a profit graph for a short put?

13. (1 point) A floor and a long call always have the same payoff.

True False

14. (4 points) The stock of Austin Auto Manufacturers currently sells for 120. The annual effective

risk free interest rate is 8.16%.

The premiums for 6 month European style calls and puts are as follows:

Strike Price Call Premium Put Premium

115 13.68 4.42

120 10.80 6.35

Chris purchases a 6 month collar on Austin Auto Manufacturers.

At the end of 6 months, Chris has a profit of zero.

Calculate the spot price at the end of 6 months.

15. (8 points) The stock of Ziad Incorporated currently sells for 48. The annual effective risk free

interest rate is 6%.

The premium for 9 month European style calls with a strike of 55 is 2.40.

Rustam enters into the long position on a 9 month synthetic forward.

Calculate the profit if the spot price of Ziad is 54 at the end of 9 months. (Remember that you

can get the premiums for a put using the put call parity formula.)

16. (2 points) Three months ago, Joe bought a 6 month European style 18 strike call option on

Huang Stock. The premium for this call option was 1.48. The annual effective risk free interest

rate is 8.243216%. The spot price at that time for Huang Stock was 17.

Today, the spot price of Huang Stock is 19.

Today, the call option is out of the money.

True False

17. (6 points) The stock of Austin Auto Manufacturers currently sells for 120. The annual effective

risk free interest rate is 8.16%.

The premiums for 6 month European style calls and puts are as follows:

Strike Price Call Premium Put Premium

115 13.68 4.42

120 10.80 6.35

125 8.36 8.73

Emily purchases a 6 month strangle on Austin Auto Manufacturers.

Determine the range of spot prices at the end of six months for which Emily will have a loss

(negative profit).

18. (3 points) There are three style of Options – American, Bermuda, and European. Write the style

of option next to each of the following situations. You do not need to use each style once.

Rehan has the right but not the obligation to purchase the stock of Bergmann Corporation for 62 at any time between now and December 31.

Brooke agrees to pay Jana 100 at the end of one year or at the end of two years if the price of gasoline is more than 4.00. However, Brooke will only make one payment. Jana can decide at the end of one year whether to require any potential payment at that time or to wait until the end of two years for any potential payment.

Surin has a put contract under which he can require Amber to make a one-time purchase 100 shares of Apple Stock for 400 per share at the end of any month for the next year.

19. (1 point) A short forward has a maximum profit when the spot price at expiration is zero.

True False

20. (7 points) Tracy purchases six futures contracts of the S&P 500 Index. The current futures price

is 1550. The futures contract is marked to market on a weekly basis.

The margin requirement on the futures contract is 8%. The maintenance margin is 60%. The

interest rate credit to the margin account is 4% compounded continuously.

At the end of the first week, Tracy gets a margin call of 5000.

Calculate the futures price at the end of one week.

21. (6 points) The current price of the stock of Mullen Company is 42.50. Mullen pays quarterly

dividends of 1.25 with the next dividend due in one month.

The annual risk free interest rate compounded continuously is 6%.

Determine the forward price for a 9 month forward contract.

22. (1 point) Draw the graph of a written straddle.

23. (5 points) The stock of Colleen’s Creations currently sells for 200. The annual effective risk free

interest rate is 3%.

The premium for 1 year European style call with a strike price of 200 is 22.65.

Qistina enters into a cap on Colleen’s Creations.

Calculate the payoff and profit if the spot price of Colleen’s Creations is 180 at the end of 1 year.

(Remember that you can get the premiums for a put using the put call parity formula.)

24. (5 points) Zach completes a short sale on the stock of Szydlo Company. The current spot price of

Szydlo stock is 123. The annual effective risk free interest rate is 7.5%.

Assume that Zach closes out his position in Szydlo stock by purchasing the stock at the end of

one year.

Complete the following payoff and profit table. If you want full credit, show your work!!

Spot Price at End of One Year

Payoff Future Value of Cost Profit

100

110

120

130

140

25. (4 points) There are five ways that futures contracts are different from forward contracts. List

four of these differences.