MN-3506: Derivatives and Risk Management MAY/JUNE 2021

发布时间：2024-06-19

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SCHOOL OF MANAGEMENT

MN-3506: Derivatives and Risk Management

DEGREE EXAMINATIONS: MAY/JUNE 2021

Question 1

A company owns 85,000 units of an asset (commodity) A and due to the uncertainty in the market decides to hedge the value of its position. As there are no future contracts available on this particular asset A, the company decides to take a position in futures contracts on another related asset B. Each futures contract is on 5,000 units. The spot price of the owned asset A is £32 and the standard deviation of the price change is estimated to be £0.58. The alternate asset B, which is intended to be used as a hedge has a futures price £30 and the standard deviation of the expected price of £0.54 over the life of the hedge. The coefficient of correlation between the spot price change and futures price change is 0.93.

Required:

a. Explain the concept of “Cross Hedge”and demonstrate what position would be taken in futures contract of alternate (related) asset to hedge. [7 marks]

b. Using the information given in question 1, Define and Measure, i, ii and iii.

i. Hedge effectiveness [5 marks]

ii. Minimum variance hedge ratio [5 marks]

iii. Optimal number of futures contracts (after tailing) [8 marks]

[Total 25 marks]

Question 2

a. Assume that the spot price of Amazon share is £2350. Amazon’s dividend is expected to be paid after 4-months of £12 per share. The continuously compounded risk free interest rate is 2% per year.

i. What should be the futures price of a 6-month contract on Amazon stock? [6 marks]

ii. The futures price is £2354, instead. Explain an arbitrage strategy, stepwise, that an investor can use to make a riskless profit. Show the calculations. [12 marks]

b. A bank finds that its assets are not matched with its liabilities. It is taking floating-rate deposits and making fixed-rate loans. Can swaps be used to offset the risk? If yes, explain how? [7 marks]

[Total 25 marks]

Question 3

The price of a European call that expires in six months and has a strike price of $30 is $2. The underlying stock price is $29, and a dividend of $0.50 is expected in two months and again in five months. Risk-free interest rates for all maturities are 10%.

Required:

a. What is the price of a European put option that expires in six months and has a strike price of $30? [10 marks]

b. Describe arbitrage opportunities if the European put price is $3. Show your working. [15 marks]

[Total 25 marks]

Question 4

a. A trader creates a bear spread by using two put options. One option has a $27 strike price with a premium of $2.35 and another put has $31 strike price costing $5.25.

Required:

Discuss what positions the trader may have taken to create the Bear spread strategy and report the initial cost of the strategy and the total payoff when the stock price in six months is $25. [7 marks]

b. An investor has a high risk tolerance and is considering to use options to employ “Straddle Strategy” . But the broker suggests her to use one of the “Strip and Strap” strategies instead.

Required:

i. When can each of these, Straddle, Strip and Strap strategies be used? In your discussion highlight the differences among the three strategies. [12 marks]

ii. Draw the payoffs from each of the strategies, Straddle, Strip and Strap (you don’t need specific numbers, just show the shapes of the payoffs). [6 marks]

[Total 25 marks]

Question 5

a. Calculate u , d , and p when a binomial tree is constructed to value an option on a foreign currency. The tree step size is one month, the domestic interest rate is 5% per annum, the foreign interest rate is 8% per annum, and the volatility is 12% per annum. [8 marks]

b. Consider an option on a non-dividend-paying stock when the stock price is $30, the exercise price is $29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months.

i. What is the price of the option if it is a European call? [7 marks]

ii. What is the price of the option if it is a European put? [7 marks]

iii. Verify that put-call parity holds. [3 marks]

[Total 25 marks]