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15.437 Spring 2014J.C. Cox

15.437 MIDTERM EXAM

Please answer any four of the five questions. If you answer all five

questions, please indicate the four that you want to have graded. Each

question is worth twenty-five points. Partial credit will be given for

incomplete answers. Be sure to write clearly and explain your answers. You

are free to use the text, your notes, and any other materials from the course,but you should not discuss the exam with anyone.

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1) Your firm is considering a two-year swap with semiannual payments.

The party that pays the fixed rate will thus make four payments during the

life of the swap. A special feature of the swap is that the party that pays the

floating rate will make no payments during the first year of the swap.

Instead, that party will pay twice the floating rate during the second year of

the swap.

The current zero coupon bond prices implied by swap rates are shown

in the table below.

Years to Maturity .5 1.0 1.5 2.0

Zero Coupon Price .99 .98 .97 .95

What is the proper fixed rate for this swap?

2) Three years ago your company entered into an eight-year swap with

semiannual payments and a principal of $100,000,000. Your firm receives a

fixed rate of 5% and pays the floating rate. The swap now has five years

remaining. The current fixed rate for newly initiated five-year swaps with

semiannual payments is 4%. The current price of a five-year zero coupon

bond is $.82 . What is the current value of your firms swap?

3) You now own a thirty-year par bond paying 10% annual coupons and

having a principal of $100. The current forward price for a one-year forward

contract on this thirty-year bond is $98. The current price of ABC stock is

$50 per share. The stock does not pay dividends. The current forward price

for a one-year forward contract on one share of stock is $54. Both forward

contracts are cash settled. Explain carefully how you could use the forward

contracts to effectively transform your $100 fixed income investment into a

$100 equity investment over the next year while continuing to hold the bond.

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One year from now your portfolio should have the same value that it would

have if you sold the bond today and invested the $100 in ABC stock.

4) Two types of forward contracts on oil are available. Each has three

years until the delivery date. One type is a standard forward contract. With

this contract, the seller delivers 100 barrels of oil and receives from the buyer

a payment equal to the forward price for each barrel delivered. The other

type provides the seller with some flexibility. Here the seller may deliver any

amount from 75 barrels to 125 barrels in fulfillment of the contract. As

before, the seller receives from the buyer an amount equal to the forward

price for each barrel delivered. With each type of contract, the forward price

is set so that no money changes hands initially.

Three-year European options, each covering one barrel of oil, can be

bought or sold on the following terms:

Striking Price Call Price Put Price

80 40 24

100 32 32

120 28 44

Based on this information, what is the proper forward price for the standard

forward contract? What is the proper forward price for the flexible forward

contract?

5) There is a market in special puts and calls on DEF stock with an

expiration date one year from now. These options are identical to ordinary

European options except for one feature. Their striking prices, instead of

being fixed, are equal to the value of one share of XYZ stock. The current

price of DEF is $90 per share, and the current price of XYZ stock is $100 per

share. Neither stock pays dividends. The current price of a zero coupon bond

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maturing one year from now is $.90. If the put is selling for $15, what should

be the price of the call?