Research School of Finance, Actuarial Studies and Statistics
FINM2002 DERIVATIVES / FINM7041 APPLIED DERIVATIVES
FINAL EXAM
Semester 2, 2022
Writing Time:
210 minutes + 5 extra minutes for Integrity Declaration
Exam Conditions:
Wattle-based
Permitted Materials:
Material on Wattle + Excel. Search on internet not allowed. Content not covered in course material will receive
zero credit.
Instructions to Students:
1. It is not permitted to disclose, disseminate, reproduce, or publish any portion of this assessment in any manner.
2. This assessment consists of a total of FIVE questions with subparts. Questions are of unequal value, with marks
indicated for each question. Please answer all questions.
3. All answers must be typed and provided within the Wattle exam interface. Only answers submitted and typed
within the answer space will be read and graded.
4. Incorrect choices for multiple-choice questions will be penalized.
5. Please show all working for marks. An answer without intermediate steps and explanations will be awarded a
mark of zero.
6. Emailed answers will not be accepted.
7. Please keep all decimal places for interim and final numerical answers, unless otherwise instructed.
8. Please remember to save your answers often by clicking either “next page” or “previous page” as per the
discussion on how to prepare for Test 1 in Lecture 4, including how to work with Wattle quiz interface.
Total Marks = 100
This exam counts towards 60% of your final grade for the course.
QUESTION 1. This question has 8 subparts, please answer all subparts. (TOTAL 16 MARKS)
I. A Treasury bond with a principal of $100 million providing quarterly floating-rate coupons has a
remaining life of 8 months. The LIBOR rate for all maturities with continuous compounding is 8% p.a.
The 3-month LIBOR three months, two months, and one month ago was 7.8% p.a.c.c, 7.9% p.a.c.c, and
7.96% p.a.c.c. What is the interest rate we need to use to calculate the next coupon (2 mark)
a. 8%
b. 7.8%
c. 7.9%
d. 7.96%
II. When we are trying to fully hedge an equity portfolio against broad market volatility, we are
effectively trying to achieve which of the following (2 marks)
a. Beta_portfolio = 1
b. Beta_portfolio = 0
c. Beta_portfolio = 0.5
d. Beta_portfolio = -1
e. Beta_portfolio = 2
f. Delta_portfolio = 0
III. Which of the following is(are) correct Select all that apply. (2 marks)
a. Different index derivatives have different contract multipliers.
b. In the case of a futures contract on the S&P/ASX 200 Index, the index multiplier is A$25 per index
point.
c. Index derivatives are quoted in points because the underlying indices are stated in points.
d. In the case of an options contract on the S&P/ASX 200 Index, the index multiplier is A$10 per index
point.
IV. Companies AB1 and XY1 are each planning on borrowing $100M for 5 years. Company AB1 can
borrow at the floating rate LIBOR and at a fixed rate of 5%, and Company XY1 can borrow at the
floating rate LIBOR+1% and a fixed rate of 8%. Company AB1 wishes for a floating-rate loan, and
Company XY1 wishes for a fixed-rate loan. If the two companies enter into an interest rate swap, and
gains for the firm with the absolute advantage in the rates is 4 times the gains to the other firm, what
rates would each firm end up paying (2 marks)
a. AB1: LIBOR-1.6%, XY1: 7.6%
b. AB1: LIBOR-0.4%, XY1: 6.4%
c. AB1: LIBOR-3.2%, XY1: 7.2%
d. AB1: LIBOR-0.8%, XY1: 4.8%
V. A 3-month call option on a non-dividend paying stock has a market price of $2.50. You are trying to
find the implied volatility from trial and error using the BSM model. With a guess of 30% for volatility,
you obtain $2.32 from the model. Which of the following guess should be your next try (2 marks)
a. 30%
b. 35%
c. 10%
d. 25%
VI. Which of the following is/are correct Select all that apply. (2 marks)
a. It was reported Bill Hwang would have had likely set aside cash buffer to post margin if needed for
his TRS positions, but the collapse in his portfolio as a result of price declines in the stocks he was
exposed to proved to be too fast and too large for the margin calls to be met.
b. The prime brokers that sold the TRS to Archegos became nervous when Archegos could not pay
margin calls and started to sell the stocks underlying the associated TRS contracts, causing further price
depreciation in those stocks and worsened Archegos’ crisis.
c. Consider an option that pays the holder the maximum between 0, and the highest stock price
achieved by XYZ within a 7-month period. This option is path-independent.
d. Ben purchases a ‘put on call’ compound option. This is reasonable if Ben is expecting the underlying
asset price to decrease before the expiry of the first option, and then decrease before the expiry of the
second option.
VII. Which of the following is/are correct Select all that apply. (2 marks)
a. A 5×8 option contract for June 2021 on electricity with monthly exercise is worth more than a 5×8
option contract for June 2021 on electricity with daily exercise. This is because the daily exercise
contracts offers more flexibility than the monthly exercise contract does, but is otherwise identical.
b. If the maximum temperature during a day is 73°F, the minimum temperature is 62°F and the median
temperature is 69°F, then the daily HDD is 2.5.
c. Company Y has entered into a reinsurance contract that provides them coverage on a pro rata basis
of 80% of their exposure for flood relates damages. If this company incurs flood related damages of
$130m, then the reinsurer is liable to pay $26m.
d. Crude oil futures can only be cash settled.
VIII. Which of the following is/are correct Select all that apply. (2 marks)
a. It is permitted to use public information to guide investment decisions.
b. Trading on material non-public information is permitted, and it improves investor confidence in the
integrity of capital markets.
c. The defined pension funds in the UK suffered due to sudden interest rate increases because they
were typically paying the floating rate in their interest rate swaps.
d. Integrity is expected both at school and at work. For example, Goldman Sachs fired junior analysts
who cheated on their online tests because such conducts are inconsistent with the code of ethics
expected of finance professionals.
QUESTION 2. This question has 3 subparts, please answer all subparts.（TOTAL 30 MARKS）
I.
It’s June, an oil refiner plans to buy 10,000 bbl. of crude oil in December. The spot price of oil is
$96/bbl. Suppose the refiner plans to hedge with December futures on crude oil at $90/bbl and plans
to close out the contract just before the delivery period. Explain the hedge’s set-up and effectiveness
for the refiner if crude oil price in December turned out to be $85. (7 marks)
II. You are a trader for StableFolio Ltd. One of your portfolios is short 100 calls on a stock with strike
$14, and also long 200 forward contracts on the stock. All contracts are due to expire in 9 months. The
stock is currently trading at $15, and its volatility is estimated at 25% p.a.; it pays a dividend of 3%
p.a.c.c. The risk free rate of interest is 5% p.a.c.c. How can you make this portfolio delta neutral Show
full working process for marks. (10 marks)
III. It’s June, the stock price for ACX is $102.51. ACX does not pay dividends. The December call option
on ACX with a strike price of $100 is trading at $2. The current interest rate for all maturities is 4% p.a.,
compounded quarterly. Is there an arbitrage opportunity and why If yes, identify an arbitrage strategy
without any out-of-pocket expenses that yields positive profits when the option expires. Explain all
steps and cash flows involved and show all calculations. (13 marks)
QUESTION 3. This question has 2 subparts, please answer all subparts.（TOTAL 23 MARKS）
I. It’s June, a futures contract is trading at $45, its volatility is 25% p.a. and the risk free interest rate is
6% p.a.c.c. What is the value of a December 48 European call on the futures (5 marks)
II. You want to price a 12-month European option on a stock using the binomial tree model (drawn and
labelled below). The volatility is 20% per annum and the risk-free interest rate is 1% p.a.c.c. The option
value at node D is 2.25, which is higher than the option value at node E. The stock price at node D is
$20.
a) Is this a call or a put Why (2 marks)
b) What is the strike price of the option Explain. (2 marks)
c) Calculate the remaining stock prices and option values that correspond to every node on the tree.
Complete working process must be shown for marks. (12 marks)
d) If the underlying asset is a stock that pays a dividend yield, without making any calculation, state
what needs to be adjusted to your calculation process to part (c). Write out the specific adjustment
needed. (2 marks)
QUESTION 4. This question has 2 subparts, please answer all subparts.（TOTAL 12 MARKS）
I. The CDS was initially created to help banks hedge credit risks of loans and bonds on their balance
sheet.
a) When stock investors are bearish, they could simply short the stock per their market view. Why
couldn’t banks do the same with their loans State and explain the main reason. (2 marks)
b) When Michael Burry orchestrated his “big short” during the 2000s, what positions in CDS did he
take Why would it not have been a good idea to instead short the underlying assets as a way to act on
his market sentiment (4 marks)
II. Using only information shared by Adrian, answer the following.
a) In Adrian’s guest lecture, he highlighted the existence of companies like Optiver is important for
financial markets. What kind of market participant is Optiver and what do companies like Optiver do
Why are they important And what characterises the best of them (3 marks)
b) In Adrian’s live chat, he discussed how to treat stock price data from periods such as the pandemic
when coming up with predictions for volatility. What are the main points (3 marks)
QUESTION 5. This question has 2 subparts, please answer all subparts. （TOTAL 19 MARKS）
I. Consider the following simplified option chain for stock XYZ. The table shows different strike prices
offered for options on stock XYZ, along with the corresponding European put and European call option
prices. XYZ’s current stock price is $30.50, and the options below all have a maturity of 3 months.
Call premium ($) Strike price ($) Put premium ($)
5.24 27 1.67
5.07 28 2.50
4.63 29 3.06
3.97 30 3.40
3.34 31 3.76
2.93 32 4.35
2.51 33 4.93
You wish to execute an options trading strategy using available XYZ options listed above. You believe it
is very likely that XYZ’s stock price will drop, but that the stock price is unlikely to drop below $28. At
the same time, you want to limit potential losses in case XYZ’s stock price increased instead.
a) Name suitable option trading strategies given your expectations of the stock price and need to limit
potential losses Explain why these are suitable strategies. (3 marks)
b) After considering the option trading strategies recommended in (a), you decide to use the strategy
that does not require an initial net cash outflow. Which strategy identified in (a) will you pursue
Describe which options are required, specify the strikes and positions needed and why. Also calculate
time 0 and time T net cash flows from the strategy, (i.e., consider option premium paid), assume all
positions are kept open until expiry and show supporting reasoning and calculations. (8 marks)
II. Tony, a trader who specialises in trading exotic options, has recently taken some positions in barrier
options. Specifically, his portfolio consists of positions in two exotic options that he entered 2 months
ago:
1. One down-and-in call option on ABC with a barrier of $25, strike price of $22 and 3 months to
maturity. Tony paid a premium of $0.70 for this long position.
2. One down-and-out call option on ABC with a barrier of $25, strike price of $22, and 3 months to
maturity. Tony paid a premium of $1.65 for this long position.
a) How can Tony replicate his current portfolio with a single option Explain how Tony can do so and
describe this option’s characteristics. (3 marks)
b) What should the premium be for this single option identified (2 marks)
c) Tony’s friend, Jason, holds the following portfolio of exotic options that he entered 2 months ago:
1. One down-and-in call option on ABC with a barrier of $25, strike price of $22 and 3 months to
maturity
2. One down-and-out call option on ABC with a barrier of $24, strike price of $22, and 3 months to
maturity.
Without any calculations, explain whose portfolio would have cost more to enter That is, would Tony
have paid more than Jason in total for his positions, or vice versa (3 marks)