ECON6042 Financial Derivatives 2020-21
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SEMESTER 2 TAKE-HOME FINAL ASSESSMENT 2020-21
ECON6042 Financial Derivatives
1. A U.K. firm is planning to invest in the U.S. in electric car charging stations. The overall investment costs 10 million US dollars and is paid in full at delivery in five years from now. The current exchange rate U.S. dollar to British pound is S0 = $1.25. The five-year risk-free annual interest rate (continuously compounded) is RUS = 2.5% and RUK = 4%. With this information, answer the following questions:
(a) Compute how many sterling the firm needs to set aside today in order to meet the cost of the project without incurring currency (exchange rate) risk in five years’ time. Explain how this can be achieved using the forward currency market.
(b) Explain two different risk-free investment alternatives that would allow the U.K. firm to obtain 10 million U.S. dollars at delivery of the project in five years from now.
(c) The firm has noted that the forward price of the British pound with five year delivery is $1.10. Derive an arbitrage strategy that allows to finance the project entirely with zero cost and without
bearing any risk. (N.B. All interest rates are continuously compounded.)
2. Companies A and B face the following interest rates:
|
|
Company A |
Company B |
|
Euro (fixed rate) |
5% |
x% |
|
Australian dollars (floating rate) |
LIBOR+0.5% |
LIBOR+1% |
(a) Assuming that A wants to borrow in Euro at a fixed rate and B wants to borrow in Australian dollars at a floating rate, derive
an upper bound for x that allows these companies to enter intoa profitable swap agreement.
(b) Assume now that x = 6%. Explain under what conditions, Company A would be interested in entering a swap agreement with Company B.
(c) Under the above conditions, and considering x = 6%, design a swap that is equally attractive to both companies arranged by a financial intermediary that makes a profit of 0.2% from these operations.
3. A 6-month European call option on a dividend-paying stock is currently selling for $1.75. The stock price is $58.56, the strike price is $55, and a dividend of $1.20 is expected in 2 months and 5 months. The risk-free interest rate is 3% per annum for all maturities.
(a) What opportunities are there for an arbitrageur? Detail your answer.
(b) In this market a European put option with same strike price and maturity is also available for trading. Derive the no-arbitrage price of the put option if the call option has a price of ct = $3.
(c) The European put option in the above section is trading at $3. What opportunities are there for an arbitrageur? Detail your answer.
4. 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 strangle and represent the profit function.
(c) Design a forward contract on a stock with a particular delivery price and delivery date as a combination of options on the same underlying asset.
5. 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 continu- ous 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