Section A: This section is COMPULSORY. Students have to answer ALL the parts to Question 1.

Question 1

a) Discuss the advantages and disadvantages of options and forward contracts in hedging for foreign exchange risk. (6 Marks)

b) Assume that F₁ and F₂ are two futures contracts on the same commodity with times to maturity t₁ and t₂, where t₁ < t₂. Prove that F₂ £ F₁e^{r(t2 – t1)} based on non-arbitrage assumption, where r is the interest rate (assumed constant) and there are no storage costs. For the purposes of this problem assume that a futures contract is the same as a forward contract. (6 Marks)

c) Discuss why it is more attractive to early exercise an American put option as the risk-free rate increases and volatility decreases. (6 Marks)

d) Discuss why derivatives trading in over-the-counter markets might have contributed to the 2007 to 2008 financial crisis? How the over-the-counter markets have been changed afterwards? (12 Marks)

[Total Marks: 30]

Section B: This section has THREE questions. Students should answer only any TWO questions in Section B.

Question 2

a) The current price of a stock is $55. The continuous compounded risk-free rate is 8% per annum. The stock is expected to pay a dividend of $1 in one month and four months. An investor enters into a short position in a six-month forward contract on this stock today.

i. Calculate the forward price today.

ii. Discuss the difference between forward pricing for investment assets and forward pricing for consumption assets. (10 Marks)

b) The current stock price is $75.00 and a six-month European call option with a strike price of $78.00 costs $2.5. An investor has $7,500 to invest.

i. What are two alternative trading strategies for this investor?

ii. In which situation can both strategies make the same profits?

iii. Distinguish different situations and compare the profit or loss of each strategy in each situation. (15 Marks)

c) A stock price is currently $5. It is known that at the end of six months, it will be either 4 or 7. The risk free rate is 12% per annum with continuous compounding. Suppose that S_T is the stock price at the end of six months. What is the value of a derivative which pays S_T³ six months later? (10 Marks)

Question 3

a) Suppose that a portfolio is worth $50 million and the S&P 500 is at 1000. The portfolio has a beta of 4.0, the risk-free interest rate is 8% per annum, and the dividend yield on both the portfolio and the index is 2% per annum. What options should be purchased to provide protection against the value of the portfolio falling below 45 million in one year’s time? (15 Marks)

b) Consider a position consisting of a $1,000 investment in gold and a $1,200 investment in silver. Suppose that volatilities of these two assets are 15% p.a. and 22% p.a., respectively. The coefficient of correlation between their returns is 0.75. What is the 10-day 95% value at risk for the portfolio? What is the diversification benefit for the portfolio? (10 Marks)

c) The spot price of the stock is $25. The volatility of the stock is 25% p.a. The continuous compounded risk-free rate is 10% p.a. The stock will pay yield at 2% p.a.

i. Calculate the value of a European put option to sell this stock at $23 in 6 months.

ii. Calculate the value of a European call option to buy this stock at $23 in 6 months using the put-call parity. (10 marks)

Question 4

a) The current stock price is $25. Over each of the next two three-month periods, it is expected that the stock price will increase by 15% or decrease by 12%. The continuously compounded risk-free rate of interest is 8% per annum.

i. What is the risk-neutral probability of an up state?

ii. What is the price for a six-month European put option with a strike price of $28? Please show the two-step binomial tree.

iii. What is the price for a six-month American put option with a strike price of $28? Please show the two-step binomial tree. (20 Marks) 

b) A European call option and put option on a stock both have a strike price of $30 and an expiration date in 3 months. Both sell for $3. The risk-free rate is 5% per annum. The current stock price is $32, and it pays continuous dividend yield at 1% per annum. Identify whether there is any arbitrage opportunity. (10 Marks)

c) An investor enters into a short position in two futures contracts on gold at $1850 per oz in three months. The contract size is 100 oz per contract. The initial margin requirement is $4950 per contract. The maintenance margin is $4500 per contract.

i. Under which circumstances could $2,000 be withdrawn from the margin account?

ii. Under which circumstances would the investor receive a margin call? (5 Marks)