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ACFI310 Derivative Securities
创建日期：2024-06-08 15:07:44
所属分类：会计Accounting
标签： ACFI310
Derivative Securities

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ACFI310 

Derivative Securities
INSTRUCTIONS TO CANDIDATES
• This is a 24-hour assessment. You are allowed to use a calculator. You should not use
the internet to ‘google’ your answers.
• For questions in Part A of the final exam, all parts are compulsory. Please type your
answers using Microsoft Word.
• For questions in Part B, you should answer TWO questions out of THREE. For those two
questions you choose, you should answer all parts.
• Please include your student ID but not your name in your answer as your work is marked
anonymously.
Student declaration:
I confirm that I have read and understood the University’s Academic Integrity policy. I confirm that
I have acted honestly, ethically and professionally in conduct leading to assessment for the
programme of study. I confirm that I have not copied material from another source nor committed
plagiarism nor fabricated data when completing the attached piece of work. I confirm that I have
not previously presented the work or part thereof for assessment for another University of
Liverpool module. I confirm that I have not colluded with any other student in the preparation and
production of this work. I confirm that I have not incorporated into this assignment material that
has been submitted by me or any other person in support of a successful application for a degree
of this or any other University or degree awarding body. Students who require sympathetic marking
should ensure that they attach the Sympathetic Marking Indicator to the first page of the document
prior to submission
Paper Code: ACFI310 Page 2 of 10
JANUARY EXAMINATIONS 2023
ACFI310 Derivative Securities
Section A: This section is COMPULSORY. Students have to answer ALL the parts
to Question 1.
Question 1
a) Explain the relationship between volatility and European call option prices. (6 marks)
b) Distinguish between the forward price and initial set up value of a forward contract. (6 marks)
c) Distinguish Value-at-Risk with Expected Shortfall. (6 marks)
d) Explain why Delta hedging a written option involves a “buy high, sell low” trading rule. (6 marks)
e) What is the volatility curve if the left tail is heavier than the lognormal distribution and the right tail
is less heavy than the lognormal distribution? (6 marks)
[Total marks: 30]
Paper Code: ACFI310 Page 3 of 10
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 $25. The continuous compounded risk-free rate is 10% per annum.
The stock pays continuous dividend yield of 2% per annum. An investor enters into a long position in a
six-month forward contract on this stock today.
i. Calculate the forward price and the value of the forward contract today.
ii. Three months later, the price of the stock is $26. The risk-free rate is still 10% per annum and the
dividend yield is still 2% per annum. What is the forward price three months later? What is the value
of the long position in the forward contract three months later?
(10 Marks)
b) The current stock price is $35.00 and a six-month European call option with a strike price of $37.00
costs $1. An investor has $7000 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 $75. It is known that at the end of three months, it will be either $70 or
$80. The risk-free rate is 8% per annum with continuous compounding. A put option on this stock has a
strike price of $72 and it will expire three months later. What is the value of this put option today? Use
the no arbitrage argument.
(10 Marks)
[Total marks: 35]
Question 3
a) Suppose that a portfolio is worth $20 million and the S&P 500 is at 1000. The portfolio has a beta of
3.0, the risk-free interest rate is 8% per annum, and the dividend yield on both the portfolio and the
index is 1% per annum. What options should be purchased to provide protection against the value of
the portfolio falling below $16 million in one year’s time?
(15 Marks)
b) Consider a position consisting of a $1,200 investment in gold and a $1,500 investment in silver.
Suppose that volatilities of these two assets are 12% p.a. and 18% p.a., respectively. The coefficient of
correlation between their returns is 0.5. What is the 10-day 99% value at risk for the portfolio? What is
the diversification benefit for the portfolio?
Paper Code: ACFI310 Page 4 of 10
(10 Marks)
c) The spot price of the stock is $30. The volatility of the stock is 20% p.a. The continuous compounded
risk-free rate is 5% p.a.
i. Calculate the value of a European call option to buy this stock at $28 in 3 months if the underlying
stock pays no dividend.
ii. Calculate the value of a European call option to buy this stock at $28 in 3 months if the underlying
stock pays a continuous dividend yield at 2% p.a.
iii. Explain the relationship between dividend yield and European call and put options.
(10 marks)
[Total marks: 35]
Question 4
a) The current stock price is $50. Over each of the next two three-month periods, it is expected that
the stock price will increase by 15% or decrease by 10%. 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 American put option with a strike price of $51? Please show the
two-step binomial tree.
iii. Calculate delta at time 0. What does delta indicate in terms of hedging?
(15 Marks)
b) A European call option and put option on a stock both have a strike price of $25 and an expiration
date in 6 months. Both sell for $2. The risk-free rate is 6% per annum. The current stock price is $21, and
it pays continuous dividend yield at 2% per annum. Identify whether there is any arbitrage opportunity.
(10 Marks)
c) A financial institution has the following portfolio of over the counter options on sterling:
Type Position Delta of option Gamma of Option Vega of option
Call -500 0.9 1.4 1.9
Call -800 0.3 2.1 1.5
Put -600 -0.7 2.4 0.4
Call -300 -0.5 1.1 1.1
A traded option is available with a delta of 0.5, a gamma of 2.5 and a vega of 1.6.
i. What position in the traded option and in sterling would make the portfolio both gamma neutral and
delta neutral?
ii. What position in the traded option and in sterling would make the portfolio both vega neutral and
delta neutral?
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