Dec 9

Derivative Market - Advance Modeling and Strategies Problem Mellon Bank etc

Problem 1

(a) Imagine that in October 2024, Mellon Bank has the opportunity to make a $2.00 million, 8-month loan at a simple interest rate of 9.57% on a 360-day basis. Note that a contract quoted on a simple, 360-day basis has a payoff at maturity of

P (1 + (i • t) /360)

where i is the simple interest rate and -1 is the number of days to maturity.

To finance the loan without exposure to interest rate risk, Mellon Bank has the following options (all on a simple, 360-day basis):

Option 1: issue an 8-month deposit at 8.14%

Option 2: Issue a 2-month deposit at 7.05% and use a number of 3-month Eurodollar futures contracts with prices given in the table below


 

Eurodollar Futures Dealers Quotes

 

Maturity

     Dec. 2024

     Mar. 2025

      Jun. 2025

      Sep. 2025

Price

92.93

92.35

91.98

91.67


Table Notes: Eurodollar futures contract size is $1.00 million dollars.

Suppose that Mellon Bank has determined that the best option is to use the futures market in combination with the 2-month deposit. Answer the following (a) - (d).

(a) Would Mellon Bank go long or short in the futures market?

i) Long
ii) Short


Problem 1 (b) Which contracts would they buy or sell to lock in their borrowing rate over the entire loan period? Select all that apply.a) Dec. 24
a) Mar. 25
a) Jun, 25
a) Sep. 25


(C) How many of each of the contracts would be required over the entire loan period?

a) (1, 1, 1, 1) of (Dec. 2024, Mar. 2025, Jun. 2025, Sep. 2025)
 b) (2, 2, 0, 0) of (Dec. 2024, Mar. 2025, Jun. 2025, Sep. 2025)
c) (0, 2, 2, 0) of (Dec. 2024, Mar. 2025, Jun. 2025, Sep. 2025)
d) (0, 0, 2, 2) of (Dec. 2024, Mar. 2025, Jun. 2025, Sep. 2025)


Problem 1 (d) What interest rates do they lock in from the futures market over the entire loan period? Select all that apply.

a)  7.07%
b)   7.65%
c)   8.02%
d)   8.33%

Problem 2 (a)
One year from now, your firm will begin manufacturing a special government order. The manufacturing process will take one year to complete and will require the use of one million ounces of silver. The silver serves as a catalyst and will be completely recovered at the end of the process. Your firm does not normally use silver and has none in inventory. The silver market has been quite volatile, and a years price change on one million ounces could easily wipe out any profit on the contract.

With this in mind, your firm wants to rent the necessary silver rather than owning it. The chairman is thinking of the transaction in the following way: one year from now the firm will pay a rental fee and receive one million ounces of silver to use for a year. Two years from now, the silver will be returned. The chairman has indicated that he would be willing to pay a rental fee of up to 10.00% of the value of the silver based on its current price.

Your assignment is to arrange the transaction. Forward contracts, each covering one ounce of silver and having one and two years until delivery, are available with the following forward prices: $26.14 and $27.05, respectively. The current price of silver is $25.57 per ounce.

The current price of a zero-coupon bond paying one dollar one year from now is $0.81, and the current price of a zero-coupon bond paying one dollar two years from now is $0.77.

Answer the following (a) - (d), which together helps outlining a strategy.

(a) To receive the one million ounces of silver necessary for manufacturing process, what long and/or short positions to take in the one- and/or two-year forward contracts? 

i) (Long, Long) positions in (One-, Two-) year forward contracts
ii) (Long, Short) positions in (One-, Two-) year forward contracts
iii) (Short, Long) positions in (One-, Two-) year forward contracts
iv) (Short, Short) positions in (One-, Two-) year forward contracts


(b) How much should the firm invest in the two-year zero-coupon bond now? Write your answer in unit of million dollars. (Remember to check the hints if you need help.)

(c) How much should the firm invest in the one-year zero-coupon bond now? Write your answer in unit of million dollars. (Remember to check the hints if you need help.)


(d) Does the rental fee indicated by aforementioned strategy meet the chairman's expectation of staying within the 10.00% limit?

i) Yes
ii) No


Problem 3 (a)
Daiwa Bank raised $30.00 million for four years at a fixed interest rate of 7.03% by issuing a bond, and then lent the funds to Micro-Technology Inc (MTI). The loan calls for a floating interest rate that changes every year: the interest rate that MTI agreed to pay is LIBOR plus 414.00 basis points (414%). At the same time, Daiwa Bank considers entering into a four-year interest rate swap with an investment banking firm, Nomura Securities, with a notional principal amount of $30.00 million. The following four-year swap terms are available from Nomura:

Option 1: Nomura pays Daiwa Bank 7.30% every year, and every year Daiwa Bank pays Nomura LIBOR plus 150.00 basis points (1.50%).

Option 2: Daiwa Bank pays Nomura 7.23% every year, and every year Nomura pays Daiwa Bank LIBOR plus 140.00 basis points (1.40%). Answer the fallowing (a) - (e)

(a) Which swap should Daiwa Bank choose to hedge their position?

i)  Option 2
ii) Option 2

(b) What precisely is the risk that Daiwa Bank faces if it does not enter into the interest rate swap? m

i)  LIBOR increasing
ii) LIBOR decreasing


(c) What is the interest rate spread that Daiwa Bank would realize as a result of all the transactions (i.e., what is the spread between their effective borrowing and lending rates)? Write your answer in unit of percentage points.

Problem 4

The exchange rate of one Swiss franc is $1.36. The price of a 6-month U.S. zero coupon bond is $0.90, and the price of a 1-year U.S. zero coupon bond is $0.88. Forward contracts are available on the Swiss franc. The forward price is $1.31 for a 6-month forward and $1.35 for a 1-year forward.

What should be the fixed rate for a 1-year semiannual interest rate swap in Switzerland? Write your answer in unit of percentage points.


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