MN-3506 Deriviatives and Risk Management MAY/JUNE 2022

发布时间：2024-06-19

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SCHOOL OF MANAGEMENT

MN-3506 Deriviatives and Risk Management

DEGREE EXAMINATIONS: MAY/JUNE 2022

Question 1

a. A trader owns 45,000 units of an asset X. She decides to hedge the value of her position with futures contracts. But, due to unavailability of future contracts on the particular asset X, the financial advisor suggests taking a position in another related asset Y for hedging. Each futures contract is on 5,000 units. The spot price of the asset that is owned is £12 and the standard deviation of the change in this price over the life of the hedge is estimated to be £0.36. The futures price of the related asset is £11 and the standard deviation of the change in this over the life of the hedge is £0.32. The coefficient of correlation between the spot price change and futures price change is 0.97.

Required:

i. What is the minimum variance hedge ratio? Should the hedger take a long or short futures position for hedging and why? [8 marks]

ii. What is the optimal number of futures contracts when issues associated with daily settlement are and are not considered? [12 marks]

b. A company has a $40 million portfolio with a beta of 1.2. The futures price for a contract on an index is 760. Futures contracts on $250 times the index can be traded. What trade is necessary to reduce beta to 0.95? [5 marks]

[Total of Question 1: 25 marks]

Question 2

a. Explain the rate “SONIA” and its importance in the financial markets. [6 marks]

b. Briefly explain the term Forward rate. Calculate the forward rate for the third year for the data given below:

The three-year zero rate is 5.7%

The four-year zero rate is 6.3%.

All rates are continuously compounded. [7 marks]

c. A one-year long forward contract on a non-dividend-paying stock is entered into when the stock price is $36 and the risk-free rate of interest is 10% per annum with continuous compounding. What are the forward price and the initial value of the forward contract at T0 , when the contract is entered? Six months later, the price of the stock is $41 and the risk-free interest rate is still 10%. What are the forward price and the value of the forward contract in six-months? [12 marks]

[Total of Question 2: 25 marks]

Question 3

a. A European put option is priced £0.90, on a non-dividend paying stock when the stock price is £14.30, the strike price is £15.65, the time to maturity is three months, and the risk free rate of interest is 9% per annum. Calculate the lower bound for the option price. Are there any arbitrage opportunities available based on the upper and lower bounds? [7 marks]

b. Based on the theoretical lower bound for put price in (a), show how riskless profit can be made using an arbitrage opportunity? In explaining the strategy show:

i) the actions the investor will have to take now [6 marks]

ii) the actions the investor will have to take after three months when the stock price is assumed to be “14” or “16” . [12 marks]

[Total of Question 3: 25 marks]

Question 4

A stock price is currently $20. Over each of the next two three-month periods the volatility in the stock price is 30%. The risk-free interest rate is 4% per annum with continuous compounding.

Required:

i. What is the value of a six-month European put option (on the underlying stock) with a strike price of $21? Use a two-step binomial tree to demonstrate the stock price and option price at each node. Include the tree diagram. [18 marks]

ii. If the put option were American, would it ever be optimal to exercise it early at any of the nodes on the tree? [7 marks]

[Total of Question 4: 25 marks]

Question 5

Company A wishes to borrow U.S. dollars at a fixed rate of interest. Company B wishes to borrow sterling at a fixed rate of interest. They have been quoted the following rates per annum (adjusted for differential tax effects):

	Sterling	US Dollars
Company A	11.0%	7.0%
Company B	10.6%	6.2%

Required: Design a swap that will net a bank, acting as intermediary, 10 basis points per annum and that will produce a gain of 15 basis points per annum for each of the two companies. Explain how a currency swap works and the typical uses of a currency swap.

[Total of Question 5: 25 marks]