ECON6042 Financial Derivatives 2018-19
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SEMESTER 2 EXAMINATIONS 2018-19
ECON6042 Financial Derivatives
1. A U.K. firm has signed an agreement to construct an oil refinery in the U.S. in five year’s time. Most of the staff and equipment will have to be hired locally in Philadelphia where the plant is going to be built. This is why the company decides to estimate the cost of the project in U.S. dollars. The Chief Financial Operator has estimated this cost to be 10 million U.S. dollars to be paid in five years’ time. The five year risk-free annual interest rate is Rus,5 = 4% in the U.S. and Ruk,5 = 2.5% in the U.K. The current spot exchange rate is 1.40 U.S. dollars per British pound. With this information, answer the following questions:
(a) Compute how much sterling the firm needs in five years’ time to meet the cost of the project without incurring currency (exchangerate) risk. Explain how this can be achieved using the forward currency market.
(b) Compute the minimum amount of sterling needed by the corpo- ration at time 0 for meeting the costs of the project and avoiding at the same time any sort of currency risk.
(c) The small team of financial engineers of the firm has noted that the forward price of sterling with five year delivery is $1.45. They
think they can develop an arbitrage trading strategy that allows them to finance the project with zero cost and without bearing any risk. Can you help them develop this strategy? Explain your answer.
(N.B. All interest rates are continuously compounded.)
2. Banks in the U.S. and Japan offer different borrowing conditions to firms A and B. The headquarters of A are based in the U.S. and the headquarters of B are located in Japan. The turnover of Company A is however several times larger than the turnover of Company B making it more creditworthy in both loan markets. The exchange rate between US dollar and Japanese yen is at time 0 equal to S0 = 0.01 US dollars per yen. These companies are interested in a one-year loan in the US market of 1 million US dollars or, alternatively, in the Japanese loan market of 100 million Japanese yen. These companies have been offered the following interest rates per annum on these loans:
|
|
U.S. |
Japan |
|
Company A Company B |
3% 5% |
x% 4.5% |
(a) Discuss under what conditions it makes sense for Companies A and B to enter into a swap agreement. Include in your discussion
potential values of x.
(b) Assume now that x = 1.5% and Company A wishes to borrow in the U.S. market. Design a swap that is equally attractive to both companies arranged by a financial intermediary that makes no profit from these operations.
(c) The Chief Financial Operator (CFO) of Company A has asked the company’s financial division to be more specific about the terms of the swap obtained in (b), in particular, they want to know the initial value of the swap that exchanges cash flows every six months. The yield curve in the U.S. and Japan is flat for the year and such that Rus,0.5 = 3% and Rus,1 = 3%; RJ,0.5 = 1.5% and
RJ,1 = 1.5%.
Copyright 2019 v01 ○c University of Southampton
(N.B. All interest rates are continuously compounded)
3. Answer the following questions on exotic options:
(a) Discuss the differences between a combination and a spread when
constructing portfolios of options.
(b) Define a long straddle and represent the profit function.
(c) Use the put-call parity relationship to relate the initial investment for a bull spread created using calls to the initial investment for a bull spread created using puts.
4. Answer the following questions on binomial trees:
(a) A stock price is currently selling at $80. Over each of the next two 6-month periods it is expected to go up by 4% or down by 5%. The risk-free interest rate is 10% per annum with continuous compounding. What is the value of a 1-year European call option
with a strike price of $75?
(b) With this information, what is the value of a 1-year European put option with a strike price of $75? Verify that the European call and European put prices satisfy the put-call parity relationship.
2022-05-18