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Name: ______________________________________ (3 points)
FIN 441
Final Exam
Your exam must be hand-written (on the PDF format provided) or
typed/printed on the computer. Write your answer in the space provided.
Do not use extra paper. When you reformat the exam from the Word file,
you must use a font size of 12 or larger, number of pages must be limited to
7, and must leave 1 inch margin on all sides. If your exam is more than 7
pages, only the first 7 pages will be read and graded. You must show
calculations in detail for numerical questions to earn credit. Email a PDF
copy to the instructor by 11:00 pm, Monday, Dec 7th. Penalty for late exams
is 5 points for every 15 minutes.
Short essay questions: Each question is worth 4 points.
1. What is the primary distinction between exchange-listed and over-the-counter
options? Which option strategy uses both markets?
2. Explain why there is or isn’t cash payment upfront in (a) an option and (b) a futures
contract.
3. Would an American call be worth more than its European counterpart if the stock
(a) does pay dividend and (b) does not pay dividend? Explain.
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4. Would an American put be worth more than its European counterpart if the stock
(a) does pay dividend and (b) does not pay dividend? Explain.
5. What is (are) the purpose(s) of instituting limits on option trading? What are these
called? What risk does an exchange face with these limits?
6. How does change in interest rates leads affect call and put prices? What would be the
direction of price changes for call and put? Explain in words without using any
equation(s).
7. Is there an arbitrage opportunity if the futures price exceeds the spot price plus
carrying cost? If so, design a trading strategy. Do not give an example.
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8. What risk is there for holding onto a futures position in the delivery month? How
does a trader avoid this risk?
9. An investor currently owns a portfolio of stocks and expects that the stock market to
fall next quarter. How does the investor hedge risk without selling the portfolio?
10. How does a borrower reduce interest rate risk?
11. Explain the difference between a recombining and non-recombining tree. Which one
is more desirable? Explain why?
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Numerical questions:
12. You calculated the following values for a two-year in-the-money American put with
$8 intrinsic value on a non-dividend paying stock currently trading at $102:
Su = $127.50 Sd = $81.60
Assume n = 2, the risk-free rate is 8% per annum, and the stock is expected to grow
at the same rate for the next two years. (12 points)

(a) Calculate the stock prices after two years.
(b) Calculate p and (1 – p) rounding them to two-digit after decimal.

(c) Calculate Pu2, Pud, Pd2, Pu, and Pd.
(d) Calculate current price of the put.

(e) Calculate the time value of the put, the initial and subsequent hedge ratios,
and the rate of return for a hedged portfolio if the stock goes down after
one period.
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13. A farmer currently holds 5,000 bushels of corn. The local mill is offering a price
of $3.41 per bushel. Currently, a four-month futures contract is trading at $3.49.
The farmer is considering selling now or holding the corn in inventory and selling
a futures contract now. The farmer can store and insure the corn at a cost of 15
cents per bushel per annum to be paid monthly in advance at the beginning of
each month. Interest rates are 7%, continuously compounded.
(10 points)
(a) Calculate total carrying cost per bushel of corn.

(b) What is the theoretical price for a four-month futures contract?

(c) What is the best strategy for the farmer? Explain why.

(d) What is the basis today?
14. A stock currently trading at $112 pays a $5 dividend in five months and eight
months. A call option on the stock with an intrinsic value of $7 expires in nine
months. Annualized yield for T-bill for this option is 8% and annualized standard
deviation (volatility) of the continuously compounded return on the stock is 13%.
(8 points)
(a) Compute S0′
(b) Compute d1 and N(d1)
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(c) Compute N(d2) assuming d2 is -.2953. Use this N(d2) in part (d).
(d) Compute the price of the European call.
15. Under the terms of an interest rate swap, PDX Corp has agreed to receive 12% per
annum and to pay six-month LIBOR in return on a notional principal of $190
million with payments being exchanged every six months. The swap has a remaining
life of 14 months. The six-month LIBOR yield curve is downward sloping and rates
for next payment dates are 14%, 16%, and 12% per annum with continuous
compounding. The six-month LIBOR at the last payment date was 11.5% per annum.
(9 points)
(a) What is the value of the fixed-rate bond?
(b) What is the value of the floating-rate bond?
(c) What is the value of the swap to PDX’s counterparty?
16. Companies P and Q have been offered the following rates per annum on a $100
million six-year loan:
_________________________________________
Fixed Rate Variable Rate
_________________________________________
Company P 11% LIBOR + 1.5%
Company Q 14% LIBOR + 2.5%
_________________________________________
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Company P requires a floating-rate loan; Company Q requires a fixed-rate loan. A
broker will charge 1.5% per annum in a swap between P & Q.
(a) Calculate net gain from swap for each company.
(b) What rates of interest will P and Q end up paying after the swap and how?
(c) Diagrammatically present the swap in a figure. (8 points)
17. Suppose that 12-month and 15-month LIBOR are 8% and 11% with continuous
compounding. ABC Inc. enters into a FRA with XYZ Inc. to receive the forward
market rate and pay 13% measured with quarterly compounding, on a notional
principal of $13 million for 3 months beginning 12 months from now. (5 points)
(a) Which party is the FRA seller and the FRA buyer?
(b) What is value of this FRA to the FRA buyer?
18. Today is February 25th, 2020, and a 1-yr T-bill is selling at 89.58% of par. A put
option on XYZ stock expires on March 14th, 2020. Calculate the appropriate annual
risk-free rate for this option. (4 points)

Recombining-and-Non-recombining-Tree-Call-and-Put-Prices

APA

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