UNIVERSITY OF CAPE TOWN

SCHOOL OF ECONOMICS

ECO400W / ECO401W

HONOURSFINANCIAL ECONOMICS

EXAMINATION – SEPTEMBER 2004

Futures, options, Derivatives

Date: 13 September, 2004Time: 2 ½ hoursAnswer all questionsAll questions carry equal weight

1.(a) On 1st March the price of gold is $300 and the December futures price

is $315. On 1st November the price of gold is $280 and the December futures price is $281. A gold producer entered into a December futures contracts on 1st March to hedge the sale of gold on 1st November. It closed out its position on 1st November.

What is the effective price received by the producer for the gold?

(b) A short forward contract that was negotiated some time ago will expire in 3 months and has a delivery price of R40. The current forward price for a 3-month forward contract is R42. The 3-month risk-free interest rate (with continuous compounding) is 8%.

What is the value of the short forward contract?

(c) A hedger takes a long position in an oil futures contract on 1st

November, 1999 to hedge an exposure on 1st March, 2000. The initial futures price is $20. On 31st December, 1999 the futures price is $21. On 1st March, 2000 it is $24. The contract is closed out on 1st March, 2000. Each contract is on 1000 barrels of oil.

What gain is recognized in the accounting year 1st January to 31st

December, 2000?

2. An option pays off at time T where is the stock price at time T and K is the strike price. Consider the situation where K=R26 and T is 1 year. The stock price is currently R24 and at the end of 1 year it will be either R30 or R18. The risk-free interest rate is 5%.

(a) What is the risk-neutral probability of the stock rising to R30?(b) What position in the stock is necessary to hedge a short position in 1

option?(c) What is the value of the option?

3. Portfolio A consists of a 1-year zero-coupon bond with a face value of R2000 and a 10-year zero-coupon bond with a face value of R6000. Portfolio B consists of a 5.95-year zero-coupon bond with a face value of R5000. The current yield on all bonds is 10% per annum.

(a) Show that both portfolios have the same duration(b) Show that the percentage changes in the values of the two portfolios

for a 0.1% per annum increase in yields are the same.

4. A currency swap has a remaining life of 15 months. It involves exchanging interest at 14% on ₤20 million for interest at 10% on $30 million once a year. The term structure of interest rates in both the UK and the USA is currently flat, and if the swap were negotiated today the interest rates exchanged would be 8% in dollars and 11% in sterling. All interest rates are quoted with annual compounding. The current exchange rate (dollars per sterling) is 1.6500.

Decompose the swap into forward contracts and find its value to the party paying dollars.

5.

(a) Three put options on a stock have the same expiration date and strike prices of R55, R60 and R65. The market prices of the options are R3, R5 and R8, respectively.

Create a butterfly spread and construct a table showing the profit from the strategy.

(b) A European call option and a put option on a stock both have a strike price

of R20 and an expiration date in 3 months. Both sell for R3. The risk-free interest rate is 10% per annum, the current stock price is R19 and a R1 dividend is expected in 1 month.

Identify the arbitrage opportunity open to a trader.