| Category |
Online Exam |
Subject |
Management |
| University |
Swansea University
|
Module Title |
MN-3506 Derivatives and Risk Management |
| Word Count |
2000 Words |
| Academic Year |
2026 |
MN-3506 Derivatives and Risk Management Online Exam
Answer FOUR Questions ONLY
Question 1
A company holds 120,000 units of commodity X and is concerned about adverse price movements over the next three months. Since no futures contracts exist on commodity X, the firm decides to use futures on a related commodity Y as a cross-hedge. Each futures contract on commodity Y represents 4,000 units. The current spot price of commodity X is £48, and the standard deviation of its price change over the hedging period is estimated to be £0.72. Commodity Y has a futures price of £45, with an expected futures price change standard deviation of £0.67. The correlation coefficient between the spot price change of X and the futures price change of Y is 0.88.
Required:
a) Explain the meaning of a “cross hedge” and describe the type of futures position the firm should take in the futures contracts on commodity Y to hedge its exposure [7 marks]
b) Using the information given above, define and compute:
i. Hedge effectiveness [5 marks]
ii. Minimum variance hedge ratio [5 marks]
iii. Optimal number of futures contracts without daily settlement [4 marks]
iv. Optimal number of futures contracts with daily settlement [after tailing] [4 marks]
[Question 1 Total: 25 marks]
Question 2
a) A company expects to refinance a £3.5 million floating-rate loan in three months, with the rate set off SONIA for the following three-month period. The firm is concerned that SONIA may rise before the reset date. Advise the company on whether it should use a SONIA futures contract or a Forward Rate Agreement (FRA) to hedge this interest rate exposure. Your answer must mention all key differences between the two instruments. [6 marks]
b) Horizon Manufacturing expects to borrow £8 million in two months, with the interest rate to be fixed for the subsequent three-month period. The current three-month SONIA rate is 4.2%. Show how the company can lock in this 4.2% borrowing rate using a Forward Rate Agreement (FRA). Calculate the outcome of the hedge if, in two months, the actual three-month SONIA rate increases to 5.1%. [9 marks]
c) It is 30 May, and Albemarle Ltd will receive interest on a £10 million floating-rate deposit that resets on 30 July, based on the three-month SONIA at that date. SONIA is currently 4.0%. The firm is concerned that SONIA may fall before the reset. Demonstrate how Albemarle can hedge this exposure using the three-month SONIA futures contract with a September expiry and calculate the outcome of the hedge on 30 July if SONIA falls to 3.5%.
Assume the following:
- September futures price today: 95.75
- Basis on 30 July: 50 ticks
- Notional value of one SONIA futures contract: £1,000,000
- Tick value: £12.50
- A year has 365 days and a quarter has 91 days [10 marks]
[Question 2 Total: 25 marks]
Question 3
Consider the data on American options on Apple shares in Table A to answer parts a, b and c.
Table A – Option Chain
|
Apple
|
|
Calls
|
Puts
|
|
Stock price
|
Strike price
|
Jun
|
Jul
|
Aug
|
Jun
|
Jul
|
Aug
|
|
*265
|
255
|
10.12
|
12.14
|
14.99
|
1.08
|
14.55
|
4.15
|
|
260
|
6.95
|
8.85
|
11.50
|
1.96
|
18.33
|
5.70
|
|
275
|
0.51
|
1.84
|
3.52
|
11.46
|
24.37
|
12.75
|
Note: All prices are in $ and expiry dates are for 2026.
Required
a) What are the upper and lower bounds for Apple’s put option with a July 2026 expiry and a strike price of 275? [5 marks]
b) What is the intrinsic and time value for Apple’s put option of an Aug expiry and strike price of 255? Explain intrinsic and time value. [5 marks]
c) Assume that it is June, and an investor holding Apple shares wishes to hedge against a fall in the value of those shares over the next month. Using options with an exercise price of 275, draw the payoff profiles for a covered call and protective put strategy (calculate and show on the profile the max gain/loss and the breakeven points).
[10 marks]
d) Compare and contrast covered call and protective put strategies, highlighting their purposes, costs and income, and when investors are likely to use them. [5 marks]
[Question 3 Total: 25 marks]
Question 4
A stock currently trades at £62. Over each of the next two three-month periods, the stock price is assumed to follow a multiplicative binomial model, moving either up or down in each period. A European call option on this stock has a strike price of £62 and a maturity of six months.
Table B has the data on stock price and volatility, its respective European Call option, and the risk-free interest rate. Use this information to answer parts a, b and c.
Table B
|
Current Stock Price
|
£62
|
|
Annual Standard Deviation (Volatility) of stock
|
10%
|
|
European Call Option – Strike Price
|
£62
|
|
Option Maturity
|
6 months
|
|
Option moneyness
|
At-the-money
|
|
Risk-free interest rate (compounded continuously)
|
5% p.a.
|
Required:
a) Calculate the risk-neutral probability of an upward and downward movement in the stock price. [8 marks]
b) Using the binomial model, estimate the value of a six-month European call option. [12 marks]
c) Construct a two-step binomial tree showing the possible stock price movements over the six months. Clearly label all nodes and show all numerical values. [5 marks]
[Question 4 Total: 25 marks]
Question 5
You are required to construct two option trading strategies using the options data in Table C. Based on the spreads, answer the required a, b and c.
|
Table C
|
|
1. Bull Spread (European Call Options)
|
2. Butterfly Spread (European Put Options)
|
|
Call Strike prices: $40 and $48
|
Put Strike prices: $35, $40, $45
|
|
Call Premiums: $3.10 and $1.20
|
Put Premiums: $2.80, $5.40, $9.10
|
|
Maturity: 9 months
|
Maturity: 6 months
|
Required
a) Explain the positions needed to create a Bull Spread and Butterfly spread. [2+4 marks]
b) Calculate the net cost of setting up the position for both strategies [2+2 marks]
c) Prepare a table for Butterfly spread strategy, showing the payoff, moneyness and profit for a range of final stock prices, at maturity, given below.
i. 𝑆𝑇 < 35
ii. 𝑆𝑇 = 38
iii. 𝑆𝑇 = 40
iv. 𝑆𝑇 ≥ 45
[5+5+5 marks]
[Question 5 Total: 25 marks]
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