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程序代写案例-BFC5915
时间：2021-10-31
1
BFC5915
Options, futures and risk management
Supplementary Questions
Most of these “Supplementary Questions” were written by Professor Phil Gray for the benefit of students wishing
to do extra practice on the unit material. There is nothing particularly special about them. In many cases, the level
of difficulty is similar to workshop questions. In some cases, they explore issues more deeply.
It is not necessary that you work through these questions. The material from the seminars and workshops is
sufficient. However, it makes sense to make them available to you for you to use them to further test yourself.
Derivatives concepts can be challenging – you can get on top of the concepts by challenging yourself to solve
these problems.
The smart way to use these Supplementary Questions:
When students are given questions and answers, there is a natural tendency to not do the necessary work. Some
students will read Question 1, look over the answer and then say “yes, that’s how I would have done it if I had
bothered to do the question”. They then read Question 2, look over the answer and then say “yes, that’s how I
would have done it if I had bothered to do the question”. And so on. They are fooling themselves into thinking
they actually understand the material. Not surprisingly, when they get into the exam and are given something very
similar, guess what – they can’t do it!
Therefore, in a perfect world, I would not provide answers at all. Alas, students who do the questions inevitably
want to know “if I got it correct?” For this reason, at the back of this document, I provide “Key Figure” answers.
This allows a student who has done the work to quickly check their answer to the Key Figure. And it stops students
who are too lazy to do the work from reading over the answers and fooling themselves that they really understand
it.
I recommend that you work at these questions until you get the answer provided in the KeyFigures at the back.
Full answers will be made available in due course. However, you will learn very little by simply looking at the
questions and answers without making a serious attempt to work on them.
Ultimately, it’s your choice how you utilise this material. My philosophy is to challenge my students. Provide
them with extensive material which gives them the opportunity to learn a lot. Some students embrace the
challenge, work hard and do very well. Others don’t have the same attitude and do poorly. Each student will
decide which case they fall into.
The questions are ordered/numbered roughly as follows.
Lecture Numbers
Lecture 1 100-199
Lecture 2 200-299
Lecture 3 300-399
Lecture 4 400-499
Lecture 5 500-599
Lecture 6 600-699
Please keep in mind that there are a lot of questions here. Wait for the solutions or post on the assignment
discussion forum to get help from other students.
Some of these Q&As are newly written by Christine. Inevitably, there will be some mistakes in the answers. If
you discover any issues/errors/problems, please let me know and I will fix it up.
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Question 101
Today is 1 May and the spot exchange rate AUD 1.00 = NZD 1.22. That is, one AUD buys NZD 1.22. You have
no underlying position/commitments/exposure in NZD but will merely speculate on exchange rate movements.
The six-month forward rate for AUD 1.00 = NZD 1.18.
a) If I talk about the NZD ‘strengthening’ relative to the AUD, what does this mean? To demonstrate that
you truly understand this concept, give an example of an exchange rate quote after the NZD has
strengthened.
b) If you want to speculate on the NZD strengthening relative to the AUD, will you take a long or short
forward position in NZD?
Given your answer to b), enter a forward contract on (say) NZD 100,000 at the six-month forward rate quoted
above.
c) On maturity of this forward contract in six-months’ time, the spot exchange rate is 1.3000 (i.e., AUD
1.00 buys NZD 1.30). You close out the forward position with a new transaction equal in magnitude and
opposite in sign to your original transaction in part b). Have you made a gain or loss on the forward
position? How much?
d) Ignore c). On maturity of this forward contract in six-months’ time, the spot exchange rate is 1.0500 (i.e.,
AUD 1.00 buys NZD 1.05). You close out the forward position with a new transaction equal in magnitude
and opposite in sign to your original transaction in part b). Have you made a gain or loss on the forward
position? How much?
Question 102
For each of the following scenarios, determine whether the trading behaviour is indicative of hedging or
speculation.
a) A major part of the operating expense for Virgin Blue is fuel cost. Due to the high and rising oil price,
management have decided to enter long forward contracts for oil.
b) You have a portfolio of Australian stocks. Although the Australian stock market has been doing well in
the past few years, you have heard a rumour that there will be a major correction soon. Based on this,
you have decided to short some SPI200 futures contracts.
c) The information is the same as that in part b, except that you have also heard some analysts say that the
Australian stock market is going to stand strong due to extremely good economic outlooks. After doing
some additional research and consulting your financial advisor, you think that the best move is to take
some long SPI200 futures contracts.
d) ABC Company exports a lot of goods to the United States. The payments are usually made in US dollars.
As there are signs that the American economy is slowing down, ABC management have decided not to
take any action.
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Question 103
Speculation and hedging are not restricted to the realm of derivatives trading. Ordinary trading decisions made
when buying and selling ordinary assets, such as shares, can be categorised as hedging and speculating.
In each of the following cases, determine whether the behaviour is speculation or hedging.
1a. A equities trader generates profit by buying and selling shares. Having years of experience in share trading,
the trader forecasts that the price of Virgin Blue shares will increase over the next three months. Despite already
owning 1000 VBA shares, the trader subsequently buys a further 500 more shares today. Contrary to her
predictions, the price of VBA shares actually decreases. Nonetheless, the trader decides to retain the shares with
the hope that the price will eventually correct.
2a. Following the initial decrease in the price of VBA shares, the trader feels confident that the price will not fall
any further. The trader buys a further 500 VBA shares bringing the total number of shares up to 2000. This time,
the trader predicts correctly. The price of VBA shares increases over the next 3 months, and the trader sells off
her stake in VBA, recouping the initial loss and actually generating a modest profit.
2b. Following the initial decrease in the price of VBA shares, the trader is concerned that the original purchase of
500 more shares will be viewed as a poor decision. Concerned that prices will decrease further, the trader decides
to wear the capital loss by selling 500 VBA shares at a price lower than that at which she purchased. The trader
retains 1000 VBA shares however, feeling confident that the price will not fall any further. This is her opportunity
to claw back some of the value lost and breakeven on the initial purchase. The price of VBA shares does actually
increase over the next 3 months, and the trader sells off the remaining VBA shares, recouping the initial loss and
actually generating a modest profit.
3. A commodities trader generates profit by buying and selling gold forward contracts. Having years of experience
in the commodities market, the trader forecasts that the price of gold will increase over the next three months due
to geopolitical trouble in the Middle East. With no current exposure in gold bullion, the trader enters into a long
forward contract, effectively locking in the price of gold.
4. As it turned out, the price of gold did increase with heightened tensions in the Middle East. However, it proved
to be a volatile market, with gold price bouncing up and down as the peace process played out. The trader is now
concerned she will lose any unrealised gains made on the original long forward contract. As a result, the trader
closes the original position by going short gold.
Question 104
You’ve are backpacking around Europe and had originally hoped to stay for another 6 months. Unfortunately,
your stash of Euros will only last another 3 months. You really don’t want to cut your holiday short and return to
Australia early, so you are desperate to make some fast cash.
You’ve heard that there’s good money to be made from currency speculation so have decided to give it a go. You
have an opinion that the AUD is going to strengthen relative to the EUR. The spot exchange rate is currently AUD
1.0000 = EUR 0.5860. The 3-month forward rate is quoted at AUD 1.0000 = EUR 0.6000.
a) You decide to enter into a forward contract denominated in AUD. The contract covers AUD 100,000. Will
you go long or short based on your opinion of likely exchange rate movements? In 3 months’ time, the spot
rate is AUD 1.0000 = EUR 0.6600. What is your profit or loss?
b) Repeat the speculation from part a, except this time assume that your initial forward position is denominated
in Euros. Assume the contract size is EUR 60,000.
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Question 105 (for interest only; not covered in the unit)
Today (day 0) you enter into 10 long SPI200 contracts with December delivery. The traded futures price is 4301.
Assume that your initial margin is $100,000 and your maintenance margin is $85,000. Therefore, if the balance
of your account falls below the maintenance margin of $85,000, you will receive a margin call and have to lodge
more funds with the ASX.
Over the next few days, the price of the S&P/ASX200 index moves, and so too does the quoted price for SPI200
Dec expiry futures. At the end of day 5, you close out your position by taking 10 short Dec SPI200 futures.
a) Complete the following table by calculating the daily gains/losses to you futures position, and the margin
calls (if any).
Day
SPI200
Futures Price
Daily
Gain/Loss
Margin Account
Balance
Margin
Call
0
1
2
3
4
5
4301
4320
4245
4210
4180
4200
--
$100,000
--
b) Add up the gains and losses made over the five-day period. What is the overall gain/loss from your trading
in SPI200 futures?
c) On a cashflow basis, you originally lodged a $100,000 initial margin. How much of this initial margin will
you get back at the close of day 5? Add the difference between the initial margin and the refunded margin to
the margin call paid on day 3.
d) Ignore the existence of daily marking-to-the-market. Using the day 0 and day 5 quotes for the Dec SPI200
futures contract, calculate the gain/loss from your futures trading.
Background: one of the major differences between forward and futures contacts is that the latter are “marked to
the market” on a daily basis. This is a process where, at the end of each day, the futures exchange calculates
whether you made a gain or loss today, and the amount is reflected in your margin (i.e., deposit) account at the
futures exchange. This question demonstrates the process of marking to the market, but is mainly for interest
only (in case you are interested).
Question 201
You are a business person based in Hong Kong. The spot AUD/HKD exchange rate is 6.15. That is, AUD 1.0000
= HKD 6.1500. In six months’ time, you must make a payment to a supplier in Australia. The invoice amount is
for HKD 10 million.
What is your exchange rate risk? A strengthening AUD or a weakening AUD?
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Question 202
It is November. You are based in Hong Kong. The spot AUD/HKD exchange rate is AUD 1.00 = HKD 4.2500.
In six months’ time, you must make a payment to a supplier in Australia. The invoice amount is for AUD 2.5
million.
a) What is the exposure you face?
b) You enter a forward contract covering AUD 2.5m with delivery the following May. The forward
rate is AUD 1.00 = HKD 4.30. To hedge the foreign exchange risk, will you take a long or short
forward contract?
c) What happens in May if the spot exchange rate then is (i) AUD 1.00 = HKD 3.50, (ii) AUD 1.00 =
HKD 5.00? Assume the forward contract is cash settled.
Question 203
It is 1 August and you are a Hong-Kong-based manager of an equity portfolio valued at HKD 600m. The beta of
the portfolio is 0.90. Assume that the dividend yield on the market portfolio is 6% p.a. and that the riskfree interest
rate is 3% p.a.. You wish to hedge against a market decline over the period through to November.
The Hang Seng index is at 12,300 today. HSI futures with delivery in November are quoted at 12,700. We have
seen that the SPI200 futures traded on the ASX have a standard AUD$25 multiplier. The HSI futures have a
standard multiplier of HKD 50.
a) Calculate how many HSI futures contracts are needed to hedge your portfolio.
b) If the Hang Seng index has risen to 14,000 at the end of November, calculate:
• The value of the share portfolio,
• The gain/loss on futures, and
• The net value of the above.
c) Repeat part b this time assuming the Hang Seng index is 11,500 in November.
nb: the HSI futures have a standard multiplier of HKD 50.
Question 204
Assume that, for whatever reasons, you require 1,000 barrels of crude oil next year on 31 March. Today is 24
November. The spot price of oil is $22 per barrel. The forward price for oil with 31 March delivery is $25.
You decide to enter a long forward contract covering 1,000 barrels (we will shortly see that this strategy is an
effective hedge against unfavourable movements in oil price). Calculate how much you will pay for the oil if:
a) on 31 March, the spot price of oil is $30 per barrel and you physically take delivery of the oil.
b) on 31 March, the spot price of oil is $18 per barrel and you physically take delivery.
c) on 31 March, the spot price of oil is $30 per barrel and you ‘close-out’ the forward contract, then buy
1,000 barrels on the spot market.
d) On 31 March, the spot price of oil is $18 per barrel and you close-out the forward contract, then buy
1,000 barrels on the spot market.
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Question 205
You are in charge of risk management for a major oil company. Today is 1st August and you anticipate that you
will have one million barrels of oil to sell on 30 September. Currently, the spot price for oil is $140 per barrel.
Your danger, of course, is that the price of oil will fall between now and September. To hedge, you enter a short
futures contract covering one million barrels for delivery at the end of September, with the futures price being
$145 per barrel. This effectively locks-in the sale price for your oil at $145 per barrel.
Between August and September, the price of oil swings dramatically, but just before expiry of the futures contract
in September, the spot price of oil is $180. Close to expiry, the September maturity oil futures contract will also
be quoted at $180.
Required :
a) Assume that physical delivery is possible under the terms of your futures contract. Explain what happens at
expiry of the September-maturity oil futures and how much money you receive.
b) Now assume that, rather than physical delivery, you close out your short futures position, and sell your oil on
the spot market. Describe what happens at the end of September in this case and how much money you
receive.
Question 301
Stock ABC is currently selling for $10. The riskless rate of interest is 10% per annum continuously compounded.
a) Calculate the correct forward price for delivery eighteen months from today.
b) If someone is quoting a forward price of $11, explain how you would make an arbitrage profit.
c) If someone was quoting a forward price of $15, explain how you would make an arbitrage profit.
Question 302
The Hang Seng index is currently 11,900. Assume the riskless rate of interest is 6% per annum and the dividend
yield on the HSI is 2% per annum. Both rates are continuously compounded.
a) Calculate the correct futures price for HSI futures deliverable in two years.
b) Explain how you can make an arbitrage profit if the futures contracts were quoted at (i) 13,000, or (ii)
10,000.
Question 303
The spot price of oil is $30 per barrel. Storage costs for oil are 1.5% per annum. The riskless rate of interest is 7%
per annum. Both rates are continuously compounded.
a) Describe a strategy to replicate a long forward position in 1,000 barrels of crude oil with delivery in one
year.
b) What is the net cashflow for this replicating strategy at time 0?
c) With the borrow and buy replicating strategy, what is the cashflow in one years’ time?
d) What must the 12-month forward price be set at to prevent arbitrage opportunities?
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Question 304
The spot exchange rate is HKD 1.00 = YEN 15.00. Interest rates in Hong Kong and Japan are 6% and 2%
respectively. Both rates are continuously compounded.
a) Calculate the correct forward exchange rate with delivery in one year.
b) Explain how you would capture an arbitrage profit if the quoted one-year forward rate was HKD 1.00 =
YEN 13.00.
c) Explain how you would capture an arbitrage profit if the quoted one-year forward rate was HKD 1.00 =
YEN 16.00.
In answering part b and c, assume that you enter a forward contract covering YEN 1,000.
Question 305
Calculate the correct no-arbitrage value of the following derivatives contracts. In all cases, assume 6% per annum
for the risk free rate of interest continuously compounded:
a) A forward contract to buy 10,000 barrels of oil in 18 months’ time. The spot oil price is $115 per barrel
and the storage cost is 3%.
b) A forward contract to sell 500 kgs of cattle in 10 weeks’ time. The spot price for cattle is $42 per
kilogram. The carrying cost is about 4% per annum.
c) A forward contract to buy 8,000 BCD shares in one years’ time. BCD shares are currently trading at $20.
Assume that company BCD is paying a dividend of $0.10 two months from now and another dividend
of $0.15 six months after that.
d) A forward contract to purchase an office building in 4 months’ time. It is currently valued at $400 million.
The lease is worth one million dollars per month. Assume the total cost of running the building (including
security and maintenance etc.) is $300,000 per month. [for interest only]
Question 306
Assume that the spot currency rate is such that USD 1.00 = SGD 1.20 (SGD = Singapore Dollar). The US and
Singapore riskfree rates are 2% p.a. and 1.5% p.a. respectively. What is the fair value of a 6-month forward
contract on the USD/SGD exchange rate?
Question 307
You are planning an overseas trip departing 1st December to celebrate your graduation, assuming of course that
you pass FINM3405 and don’t have to spend summer studying for a Supplementary Exam. Today is 1st September
and a quick check of the newspaper shows that the relevant exchange rate is AUD1.00 = EUR 0.5985. Your budget
suggests that EUR 10,000 will be required for your vacation.
a) What is the risk you face? If you can hedge this risk by using forward contracts, would you hold a long or
short position? If you expect that the Australian dollar is going to appreciate relative to the Euro, then in
order to hedge the risk you face, would you use a long position or short position?
b) Now assume that you decide not to hedge using forward contracts. Indeed, you decide to borrow enough
Australian dollars today so that you will get approximately EUR 10,000 three months from now. Assume
that you can borrow/invest Euro at a European bank at 5% p.a.. How much do you need to borrow? If you
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can borrow/lend AUD at a local bank at 7% p.a., then how much do you owe the local bank in AUD three
months from now?
c) Use the concept of no arbitrage, what should the quoted 3-month forward rate be?
d) If the quoted 3-month forward rate is 0.5500, explain what trades you would enact to capture the arbitrage
profit.
e) Ignore d). If the quoted 3-month forward rate is 0.7500, explain how you could make a riskless profit.
Question 308
Lecture 3 began with an example of why a forward contract for delivery of WBC in one year must be priced at
$23.13; specifically, if it trades at any other price, an arbitrage opportunity is available. That example was
simplistic in that I assumed WBC paid no dividends during the next year.
Consider the stock TST which is currently trading at $10 and is expected to pay a dividend of $0.90 in exactly
five months’ time. The riskfree rate of interest is 6% pa.
A forward contract is written to deliver 1,000 TST shares in nine months’ time.
Required:
a) Calculate the no-arbitrage price of this forward contract.
b) Assume you have found someone willing to enter into a nine-month forward contract on TST at a delivery
price of $9.80. Explain what trades you would execute to capture the arbitrage opportunity.
c) Assume you have found someone willing to enter into a nine-month forward contract on TST at a delivery
price of $9. Explain what trades you would execute to capture the arbitrage opportunity.
Question 309
Today is the 1st of August. You are a financial officer for Goldtech, a US-based technology company. Goldtech
specialises in the manufacture of gold based alloys for electrical components. The company just won a tender with
a multinational computer hardware producer for the manufacture of gold based electrical components. Work is
expected to commence on the 1st of December this year.
The production manager is estimating that the company will require 2,000 ounces of gold in order to meet the
obligations underlying the contract. This quantity of gold must therefore be on hand when production starts in
December. The maximum amount the company can afford to spend on gold is $2m. Anything greater than this
and the tender will begin to be unprofitable.
At the spot price of gold is $850 per ounce, the tender is viable. However, you are concerned that the price per
ounce of gold will increase between now and the commencement of production. There are a number of courses of
action available to you and we will explore the outcomes of each.
a) Assume you do nothing. In December, the day before commencement of production, you purchase the gold
from the spot market a price of $1200 per ounce. How much will 2,000 ounces of gold cost you?
b) Rather than risking the adverse consequences of a gold price increase, we simply purchase 2,000 ounces of
gold today at a spot price of $850 per ounce place the gold in a storage facility and hold onto the gold until
production starts in December. Assume that there are no storage costs for the gold. How much does the gold
cost?
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c) While you like the idea from part b of buying the gold today, you don’t have sufficient cash to be buying it
so far in advance of the production date. Instead, you borrow enough money from a bank to buy the gold
today. Assume that the borrowing cost is 8% pa. Again, assume zero storage costs. The effective cost of the
gold is the payout figure on the loan. How much is it?
d) Continuing on from part c, now assume that there is a storage cost for the gold. The bank that loans you the
cash also offers a secure vault to store your gold at a storage cost of 3% pa. What is the effective cost of gold
in this case?
e) Gold futures are traded on the New York Mercantile Exchange. Calculate the fair price for the delivery of
gold on 30 November. Assume that you use these gold futures to hedge the price risk. Will you go long or
short? What is the effective cost of the gold using the futures contracts?
f) If the quoted futures price for November delivery gold was in fact $900 per ounce, there is an arbitrage
opportunity available. Describe how to take advantage of this opportunity and quantify the profit for 2,000
ounces of gold.
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Question 401
For each of the following option positions, calculate:
• The cashflow paid or received today on entering the position,
• Whether you want the price of the underlying share to go up or down,
• The breakeven share price for the position,
• Whether or not you will exercise the option,
• The gross payoff at expiry, and
• The net payoff at expiry.
a) You enter a long position in a call option. The strike price is $20 and the option premium is $0.35. At expiry,
the price of the underlying share is $15.
b) You enter a long position in a call option. The strike price is $20 and option premium is $0.35. At expiry, the
price of the underlying share is $18.
c) You enter a long position in a call option. The strike price is $20 and option premium is $0.35. At expiry, the
price of the underlying share is $20.20.
d) You enter a long position in a call option. The strike price is $20 and option premium is $0.35. At expiry, the
price of the underlying share is $20.35.
e) You enter a long position in a call option. The strike price is $20 and option premium is $0.35. At expiry, the
price of the underlying share is $21.
f) You enter a long position in a call option. The strike price is $20 and option premium is $0.35. At expiry, the
price of the underlying share is $21.50.
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Question 402
For each of the following option positions, calculate:
• The cashflow paid or received today on entering the position,
• Whether you want the price of the underlying share to go up or down,
• The breakeven share price for the position,
• Whether or not you will exercise the option,
• The gross payoff at expiry, and
• The net payoff at expiry.
a) You enter a short position in a call option. The strike price is $20 and option premium is $0.35. At expiry,
the price of the underlying share is $15.
b) You enter a short position in a call option. The strike price is $20 and option premium is $0.35. At expiry,
the price of the underlying share is $18.
c) You enter a short position in a call option. The strike price is $20 and option premium is $0.35. At expiry,
the price of the underlying share is $20.20.
d) You enter a short position in a call option. The strike price is $20 and option premium is $0.35. At expiry,
the price of the underlying share is $20.35.
e) You enter a short position in a call option. The strike price is $20 and option premium is $0.35. At expiry,
the price of the underlying share is $21.
f) You enter a short position in a call option. The strike price is $20 and option premium is $0.35. At expiry,
the price of the underlying share is $21.50.
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Question 403
For each of the following option positions, calculate:
• The cashflow paid or received today on entering the position,
• Whether you want the price of the underlying share to go up or down,
• The breakeven share price for the position,
• Whether or not you will exercise the option,
• The gross payoff at expiry, and
• The net payoff at expiry.
a) You enter a long position in a put option. The strike price is $5 and the option premium is $0.50. At expiry,
the price of the underlying share is $5.40.
b) You enter a long position in a put option. The strike price is $5 and option premium is $0.50. At expiry, the
price of the underlying share is $4.80.
c) You enter a long position in a put option. The strike price is $5 and option premium is $0.50. At expiry, the
price of the underlying share is $4.50.
d) You enter a long position in a put option. The strike price is $5 and option premium is $0.50. At expiry, the
price of the underlying share is $4.30.
e) You enter a long position in a put option. The strike price is $5 and option premium is $0.50. At expiry, the
price of the underlying share is $3.80.
Question 404
For each of the following option positions, calculate:
• The cashflow paid or received today on entering the position,
• Whether you want the price of the underlying share to go up or down,
• The breakeven share price for the position,
• Whether or not you will exercise the option,
• The gross payoff at expiry, and
• The net payoff at expiry.
a) You enter a short position in a put option. The strike price is $5 and the option premium is $0.50. At expiry,
the price of the underlying share is $5.40.
b) You enter a short position in a put option. The strike price is $5 and option premium is $0.50. At expiry, the
price of the underlying share is $4.80.
c) You enter a short position in a put option. The strike price is $5 and option premium is $0.50. At expiry, the
price of the underlying share is $4.50.
d) You enter a short position in a put option. The strike price is $5 and option premium is $0.50. At expiry, the
price of the underlying share is $4.30.
e) You enter a short position in a put option. The strike price is $5 and option premium is $0.50. At expiry, the
price of the underlying share is $3.80.
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Question 405
As at 5 July 2017, QBE share price closed at $12.10. The extract below shows a range of call options available on
QBE Insurance. The “Last Sale” column indicates the price paid for the last sale of the option on the previous
day. As such, it provides an indication of what it would cost you to enter a long position (or what you would
receive if you entered a short position).
For each option series shown (i.e., for each row in the extract), indicate:
• Whether the call option is currently in the money, or out of the money, and
• What the breakeven point is.
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Question 406
As at 5 July 2017, TLS share price closed at $4.41. The extract below shows a range of put options available on
Telstra. The “Last Sale” column indicates the price paid for the last sale of the option on the previous day. As
such, it provides an indication of what it would cost you to enter a long position (or what you would receive if
you entered a short position).
For each option series shown (i.e., for each row in the extract), indicate:
• Whether the put option is currently in the money, or out of the money, and
• What the breakeven point is.
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Question 501
A trader is interested in setting up a specialised strategy by investing in put options as
indicated in the following table. All these options are written on the same underlying share
and have the same maturity. Answer part (a), (b) and (c).
Exercise price Option premium
Long 1 put $50 $3
Short 1 put $60 $5
Short 1 put $67 $8
Long 1 put $77 $12
a) Draw the net profit and loss diagram for this strategy. Show the workings and mark the
intercepts on the X- and Y- axes clearly.
b) Work out the net profit or loss for each case in the table.
The share price at maturity is: The net profit or loss is:
$48.00
$51.50
$59.00
$65.00
$76.50
c) Explain the trader’s expectation of the future share price movement of the underlying share
by adopting this strategy.
Question 502
What is meant by a protective put? Draw the diagram for a protective put with all the options
and other positions that make up the protective put. What is the equivalent position in calls
that will give the same payoff as a protective put?
Question 601
A put option is available that will give you the right to sell a single share of ABC. The option
will expire in two months time and can be exercised at any time up to the expiry date. The
exercise price is set at $10.40 with the current ABC price at $10.00. The risk-free interest
rate is 12.0% per annum. The up factor for each step is 1.06 and the down factor is 0.944.
(a) Use a two period binomial model of share price movements to estimate the possible
future payoffs from the option at expiry. Each time interval in the binomial model is
to be of length one month. Draw the stock price lattice and the lattice of intrinsic
(immediate exercise) values. Hence derive the price for purchasing the option today.
(b) Hence derive the fair value for purchasing the option today.
(c) If the option could be bought today for $0.41 would you recommend buying the
option? Give reasons for your answer.
16
(d) Discuss the strengths, weaknesses and assumptions of the binomial option pricing
model.
Question 602
You observe the shares on ABC trading at $61.00. Call and put options on ABC shares are
also trading. Each option contract is written over 1000 shares. A three month call option at a
strike price of $60.00 is trading at $3.00 while the put option is trading at $1.08. Show that
there is an arbitrage profit to be made, and give explicit details of how the mispricing will be
arbitraged and what the profit (in dollars) of your arbitrage strategy will be. You must show
the exact strategy. Assume that the risk-free rate is 4.5% p.a. (continuously compounded).
Question 603
A stock price is currently $20.00. It is known that at the end of three months it will be either
$23 or $17. The risk-free rate of interest is 5% per annum with continuous compounding.
What is the value of a three month European put option with a strike price of $20. You must
use no-arbitrage (delta hedging) arguments to calculate a riskless portfolio in order to derive
the value of the put.
17
Key Figure Answers
The full solutions to these supplementary questions will be made available in due course. The optimal way to get
the most out of these questions is to keep working on them until you solve them! That’s where the value of these
revision questions lies. There is little value in having both questions and answers and just looking through them.
Question KeyFig Answer Question KerFig Answer
Q101 c
Q101 d
Loss 7830
Profit 10,490
501 Net profit/loss:
-2,-0.50,+7.00, +8.00,-
1.50
Q104a
Q104b
Profit EUR 6,000
Profit AUD 9,090
601 Price = $0.5066
At $0.41 option is
undervalued
Q105b
Q105c
Q105d
$25,250
$97,500
$25,250
602 Call is overpriced relative
to put.
Q202ci
Q202cii
Loss 2,000,000
Profit 1,750,000
Overall cost $10,750,000
603 Put price = $1.357
Q203a
Q203b
Q203c
850 contracts
HKD 686,040,000; 55.250m loss
HKD 576,276,000;
profit 51m
Q204 Cost is $25,000 in every case
Q205a
Q205b
Receive $145m
$35m loss, ovberall cost $145m
Q301a
Q301b
Q301c
F=$11.62
$0.62 arbitrage profit
$3.38 arbitrage profit
Q302a F=12,891
Q303d F=$32,661.51
Q304a
Q304b
Q304c
F=0.0694 or F=14.4118 (equivalent!)
Arbitrage profit HKD 7.48
Arbitrage profit HKD 6.93
Q305a
Q305b
Q305c
Q305d
F = $131.6217
F = $42.8155
F = $20.9786
F = $405,259,413
Q306 0.8354 or 1.1970 (equivalent!)
Q307b
Q307c
Q307d
Q307e
Borrow AUD 16,500.88; owe AUD
16,792.19
F = 0.5955
Arbitrage profit $1,390
Arbitrage profit $3,459
Q308a
Q308b
Q308c
F = $9.54
Arbitrage profit $0.26
Arbitrage profit $0.54
Q309a
Q309b
Q309c
Q309d
Q309e
Q309f
$2.4m
$1.7m
$1,745,943
$1,763,490
$1,763,490
arbitrage profit $36,510
学霸联盟
学霸联盟
BFC5915
Options, futures and risk management
Supplementary Questions
Most of these “Supplementary Questions” were written by Professor Phil Gray for the benefit of students wishing
to do extra practice on the unit material. There is nothing particularly special about them. In many cases, the level
of difficulty is similar to workshop questions. In some cases, they explore issues more deeply.
It is not necessary that you work through these questions. The material from the seminars and workshops is
sufficient. However, it makes sense to make them available to you for you to use them to further test yourself.
Derivatives concepts can be challenging – you can get on top of the concepts by challenging yourself to solve
these problems.
The smart way to use these Supplementary Questions:
When students are given questions and answers, there is a natural tendency to not do the necessary work. Some
students will read Question 1, look over the answer and then say “yes, that’s how I would have done it if I had
bothered to do the question”. They then read Question 2, look over the answer and then say “yes, that’s how I
would have done it if I had bothered to do the question”. And so on. They are fooling themselves into thinking
they actually understand the material. Not surprisingly, when they get into the exam and are given something very
similar, guess what – they can’t do it!
Therefore, in a perfect world, I would not provide answers at all. Alas, students who do the questions inevitably
want to know “if I got it correct?” For this reason, at the back of this document, I provide “Key Figure” answers.
This allows a student who has done the work to quickly check their answer to the Key Figure. And it stops students
who are too lazy to do the work from reading over the answers and fooling themselves that they really understand
it.
I recommend that you work at these questions until you get the answer provided in the KeyFigures at the back.
Full answers will be made available in due course. However, you will learn very little by simply looking at the
questions and answers without making a serious attempt to work on them.
Ultimately, it’s your choice how you utilise this material. My philosophy is to challenge my students. Provide
them with extensive material which gives them the opportunity to learn a lot. Some students embrace the
challenge, work hard and do very well. Others don’t have the same attitude and do poorly. Each student will
decide which case they fall into.
The questions are ordered/numbered roughly as follows.
Lecture Numbers
Lecture 1 100-199
Lecture 2 200-299
Lecture 3 300-399
Lecture 4 400-499
Lecture 5 500-599
Lecture 6 600-699
Please keep in mind that there are a lot of questions here. Wait for the solutions or post on the assignment
discussion forum to get help from other students.
Some of these Q&As are newly written by Christine. Inevitably, there will be some mistakes in the answers. If
you discover any issues/errors/problems, please let me know and I will fix it up.
2
Question 101
Today is 1 May and the spot exchange rate AUD 1.00 = NZD 1.22. That is, one AUD buys NZD 1.22. You have
no underlying position/commitments/exposure in NZD but will merely speculate on exchange rate movements.
The six-month forward rate for AUD 1.00 = NZD 1.18.
a) If I talk about the NZD ‘strengthening’ relative to the AUD, what does this mean? To demonstrate that
you truly understand this concept, give an example of an exchange rate quote after the NZD has
strengthened.
b) If you want to speculate on the NZD strengthening relative to the AUD, will you take a long or short
forward position in NZD?
Given your answer to b), enter a forward contract on (say) NZD 100,000 at the six-month forward rate quoted
above.
c) On maturity of this forward contract in six-months’ time, the spot exchange rate is 1.3000 (i.e., AUD
1.00 buys NZD 1.30). You close out the forward position with a new transaction equal in magnitude and
opposite in sign to your original transaction in part b). Have you made a gain or loss on the forward
position? How much?
d) Ignore c). On maturity of this forward contract in six-months’ time, the spot exchange rate is 1.0500 (i.e.,
AUD 1.00 buys NZD 1.05). You close out the forward position with a new transaction equal in magnitude
and opposite in sign to your original transaction in part b). Have you made a gain or loss on the forward
position? How much?
Question 102
For each of the following scenarios, determine whether the trading behaviour is indicative of hedging or
speculation.
a) A major part of the operating expense for Virgin Blue is fuel cost. Due to the high and rising oil price,
management have decided to enter long forward contracts for oil.
b) You have a portfolio of Australian stocks. Although the Australian stock market has been doing well in
the past few years, you have heard a rumour that there will be a major correction soon. Based on this,
you have decided to short some SPI200 futures contracts.
c) The information is the same as that in part b, except that you have also heard some analysts say that the
Australian stock market is going to stand strong due to extremely good economic outlooks. After doing
some additional research and consulting your financial advisor, you think that the best move is to take
some long SPI200 futures contracts.
d) ABC Company exports a lot of goods to the United States. The payments are usually made in US dollars.
As there are signs that the American economy is slowing down, ABC management have decided not to
take any action.
3
Question 103
Speculation and hedging are not restricted to the realm of derivatives trading. Ordinary trading decisions made
when buying and selling ordinary assets, such as shares, can be categorised as hedging and speculating.
In each of the following cases, determine whether the behaviour is speculation or hedging.
1a. A equities trader generates profit by buying and selling shares. Having years of experience in share trading,
the trader forecasts that the price of Virgin Blue shares will increase over the next three months. Despite already
owning 1000 VBA shares, the trader subsequently buys a further 500 more shares today. Contrary to her
predictions, the price of VBA shares actually decreases. Nonetheless, the trader decides to retain the shares with
the hope that the price will eventually correct.
2a. Following the initial decrease in the price of VBA shares, the trader feels confident that the price will not fall
any further. The trader buys a further 500 VBA shares bringing the total number of shares up to 2000. This time,
the trader predicts correctly. The price of VBA shares increases over the next 3 months, and the trader sells off
her stake in VBA, recouping the initial loss and actually generating a modest profit.
2b. Following the initial decrease in the price of VBA shares, the trader is concerned that the original purchase of
500 more shares will be viewed as a poor decision. Concerned that prices will decrease further, the trader decides
to wear the capital loss by selling 500 VBA shares at a price lower than that at which she purchased. The trader
retains 1000 VBA shares however, feeling confident that the price will not fall any further. This is her opportunity
to claw back some of the value lost and breakeven on the initial purchase. The price of VBA shares does actually
increase over the next 3 months, and the trader sells off the remaining VBA shares, recouping the initial loss and
actually generating a modest profit.
3. A commodities trader generates profit by buying and selling gold forward contracts. Having years of experience
in the commodities market, the trader forecasts that the price of gold will increase over the next three months due
to geopolitical trouble in the Middle East. With no current exposure in gold bullion, the trader enters into a long
forward contract, effectively locking in the price of gold.
4. As it turned out, the price of gold did increase with heightened tensions in the Middle East. However, it proved
to be a volatile market, with gold price bouncing up and down as the peace process played out. The trader is now
concerned she will lose any unrealised gains made on the original long forward contract. As a result, the trader
closes the original position by going short gold.
Question 104
You’ve are backpacking around Europe and had originally hoped to stay for another 6 months. Unfortunately,
your stash of Euros will only last another 3 months. You really don’t want to cut your holiday short and return to
Australia early, so you are desperate to make some fast cash.
You’ve heard that there’s good money to be made from currency speculation so have decided to give it a go. You
have an opinion that the AUD is going to strengthen relative to the EUR. The spot exchange rate is currently AUD
1.0000 = EUR 0.5860. The 3-month forward rate is quoted at AUD 1.0000 = EUR 0.6000.
a) You decide to enter into a forward contract denominated in AUD. The contract covers AUD 100,000. Will
you go long or short based on your opinion of likely exchange rate movements? In 3 months’ time, the spot
rate is AUD 1.0000 = EUR 0.6600. What is your profit or loss?
b) Repeat the speculation from part a, except this time assume that your initial forward position is denominated
in Euros. Assume the contract size is EUR 60,000.
4
Question 105 (for interest only; not covered in the unit)
Today (day 0) you enter into 10 long SPI200 contracts with December delivery. The traded futures price is 4301.
Assume that your initial margin is $100,000 and your maintenance margin is $85,000. Therefore, if the balance
of your account falls below the maintenance margin of $85,000, you will receive a margin call and have to lodge
more funds with the ASX.
Over the next few days, the price of the S&P/ASX200 index moves, and so too does the quoted price for SPI200
Dec expiry futures. At the end of day 5, you close out your position by taking 10 short Dec SPI200 futures.
a) Complete the following table by calculating the daily gains/losses to you futures position, and the margin
calls (if any).
Day
SPI200
Futures Price
Daily
Gain/Loss
Margin Account
Balance
Margin
Call
0
1
2
3
4
5
4301
4320
4245
4210
4180
4200
--
$100,000
--
b) Add up the gains and losses made over the five-day period. What is the overall gain/loss from your trading
in SPI200 futures?
c) On a cashflow basis, you originally lodged a $100,000 initial margin. How much of this initial margin will
you get back at the close of day 5? Add the difference between the initial margin and the refunded margin to
the margin call paid on day 3.
d) Ignore the existence of daily marking-to-the-market. Using the day 0 and day 5 quotes for the Dec SPI200
futures contract, calculate the gain/loss from your futures trading.
Background: one of the major differences between forward and futures contacts is that the latter are “marked to
the market” on a daily basis. This is a process where, at the end of each day, the futures exchange calculates
whether you made a gain or loss today, and the amount is reflected in your margin (i.e., deposit) account at the
futures exchange. This question demonstrates the process of marking to the market, but is mainly for interest
only (in case you are interested).
Question 201
You are a business person based in Hong Kong. The spot AUD/HKD exchange rate is 6.15. That is, AUD 1.0000
= HKD 6.1500. In six months’ time, you must make a payment to a supplier in Australia. The invoice amount is
for HKD 10 million.
What is your exchange rate risk? A strengthening AUD or a weakening AUD?
5
Question 202
It is November. You are based in Hong Kong. The spot AUD/HKD exchange rate is AUD 1.00 = HKD 4.2500.
In six months’ time, you must make a payment to a supplier in Australia. The invoice amount is for AUD 2.5
million.
a) What is the exposure you face?
b) You enter a forward contract covering AUD 2.5m with delivery the following May. The forward
rate is AUD 1.00 = HKD 4.30. To hedge the foreign exchange risk, will you take a long or short
forward contract?
c) What happens in May if the spot exchange rate then is (i) AUD 1.00 = HKD 3.50, (ii) AUD 1.00 =
HKD 5.00? Assume the forward contract is cash settled.
Question 203
It is 1 August and you are a Hong-Kong-based manager of an equity portfolio valued at HKD 600m. The beta of
the portfolio is 0.90. Assume that the dividend yield on the market portfolio is 6% p.a. and that the riskfree interest
rate is 3% p.a.. You wish to hedge against a market decline over the period through to November.
The Hang Seng index is at 12,300 today. HSI futures with delivery in November are quoted at 12,700. We have
seen that the SPI200 futures traded on the ASX have a standard AUD$25 multiplier. The HSI futures have a
standard multiplier of HKD 50.
a) Calculate how many HSI futures contracts are needed to hedge your portfolio.
b) If the Hang Seng index has risen to 14,000 at the end of November, calculate:
• The value of the share portfolio,
• The gain/loss on futures, and
• The net value of the above.
c) Repeat part b this time assuming the Hang Seng index is 11,500 in November.
nb: the HSI futures have a standard multiplier of HKD 50.
Question 204
Assume that, for whatever reasons, you require 1,000 barrels of crude oil next year on 31 March. Today is 24
November. The spot price of oil is $22 per barrel. The forward price for oil with 31 March delivery is $25.
You decide to enter a long forward contract covering 1,000 barrels (we will shortly see that this strategy is an
effective hedge against unfavourable movements in oil price). Calculate how much you will pay for the oil if:
a) on 31 March, the spot price of oil is $30 per barrel and you physically take delivery of the oil.
b) on 31 March, the spot price of oil is $18 per barrel and you physically take delivery.
c) on 31 March, the spot price of oil is $30 per barrel and you ‘close-out’ the forward contract, then buy
1,000 barrels on the spot market.
d) On 31 March, the spot price of oil is $18 per barrel and you close-out the forward contract, then buy
1,000 barrels on the spot market.
6
Question 205
You are in charge of risk management for a major oil company. Today is 1st August and you anticipate that you
will have one million barrels of oil to sell on 30 September. Currently, the spot price for oil is $140 per barrel.
Your danger, of course, is that the price of oil will fall between now and September. To hedge, you enter a short
futures contract covering one million barrels for delivery at the end of September, with the futures price being
$145 per barrel. This effectively locks-in the sale price for your oil at $145 per barrel.
Between August and September, the price of oil swings dramatically, but just before expiry of the futures contract
in September, the spot price of oil is $180. Close to expiry, the September maturity oil futures contract will also
be quoted at $180.
Required :
a) Assume that physical delivery is possible under the terms of your futures contract. Explain what happens at
expiry of the September-maturity oil futures and how much money you receive.
b) Now assume that, rather than physical delivery, you close out your short futures position, and sell your oil on
the spot market. Describe what happens at the end of September in this case and how much money you
receive.
Question 301
Stock ABC is currently selling for $10. The riskless rate of interest is 10% per annum continuously compounded.
a) Calculate the correct forward price for delivery eighteen months from today.
b) If someone is quoting a forward price of $11, explain how you would make an arbitrage profit.
c) If someone was quoting a forward price of $15, explain how you would make an arbitrage profit.
Question 302
The Hang Seng index is currently 11,900. Assume the riskless rate of interest is 6% per annum and the dividend
yield on the HSI is 2% per annum. Both rates are continuously compounded.
a) Calculate the correct futures price for HSI futures deliverable in two years.
b) Explain how you can make an arbitrage profit if the futures contracts were quoted at (i) 13,000, or (ii)
10,000.
Question 303
The spot price of oil is $30 per barrel. Storage costs for oil are 1.5% per annum. The riskless rate of interest is 7%
per annum. Both rates are continuously compounded.
a) Describe a strategy to replicate a long forward position in 1,000 barrels of crude oil with delivery in one
year.
b) What is the net cashflow for this replicating strategy at time 0?
c) With the borrow and buy replicating strategy, what is the cashflow in one years’ time?
d) What must the 12-month forward price be set at to prevent arbitrage opportunities?
7
Question 304
The spot exchange rate is HKD 1.00 = YEN 15.00. Interest rates in Hong Kong and Japan are 6% and 2%
respectively. Both rates are continuously compounded.
a) Calculate the correct forward exchange rate with delivery in one year.
b) Explain how you would capture an arbitrage profit if the quoted one-year forward rate was HKD 1.00 =
YEN 13.00.
c) Explain how you would capture an arbitrage profit if the quoted one-year forward rate was HKD 1.00 =
YEN 16.00.
In answering part b and c, assume that you enter a forward contract covering YEN 1,000.
Question 305
Calculate the correct no-arbitrage value of the following derivatives contracts. In all cases, assume 6% per annum
for the risk free rate of interest continuously compounded:
a) A forward contract to buy 10,000 barrels of oil in 18 months’ time. The spot oil price is $115 per barrel
and the storage cost is 3%.
b) A forward contract to sell 500 kgs of cattle in 10 weeks’ time. The spot price for cattle is $42 per
kilogram. The carrying cost is about 4% per annum.
c) A forward contract to buy 8,000 BCD shares in one years’ time. BCD shares are currently trading at $20.
Assume that company BCD is paying a dividend of $0.10 two months from now and another dividend
of $0.15 six months after that.
d) A forward contract to purchase an office building in 4 months’ time. It is currently valued at $400 million.
The lease is worth one million dollars per month. Assume the total cost of running the building (including
security and maintenance etc.) is $300,000 per month. [for interest only]
Question 306
Assume that the spot currency rate is such that USD 1.00 = SGD 1.20 (SGD = Singapore Dollar). The US and
Singapore riskfree rates are 2% p.a. and 1.5% p.a. respectively. What is the fair value of a 6-month forward
contract on the USD/SGD exchange rate?
Question 307
You are planning an overseas trip departing 1st December to celebrate your graduation, assuming of course that
you pass FINM3405 and don’t have to spend summer studying for a Supplementary Exam. Today is 1st September
and a quick check of the newspaper shows that the relevant exchange rate is AUD1.00 = EUR 0.5985. Your budget
suggests that EUR 10,000 will be required for your vacation.
a) What is the risk you face? If you can hedge this risk by using forward contracts, would you hold a long or
short position? If you expect that the Australian dollar is going to appreciate relative to the Euro, then in
order to hedge the risk you face, would you use a long position or short position?
b) Now assume that you decide not to hedge using forward contracts. Indeed, you decide to borrow enough
Australian dollars today so that you will get approximately EUR 10,000 three months from now. Assume
that you can borrow/invest Euro at a European bank at 5% p.a.. How much do you need to borrow? If you
8
can borrow/lend AUD at a local bank at 7% p.a., then how much do you owe the local bank in AUD three
months from now?
c) Use the concept of no arbitrage, what should the quoted 3-month forward rate be?
d) If the quoted 3-month forward rate is 0.5500, explain what trades you would enact to capture the arbitrage
profit.
e) Ignore d). If the quoted 3-month forward rate is 0.7500, explain how you could make a riskless profit.
Question 308
Lecture 3 began with an example of why a forward contract for delivery of WBC in one year must be priced at
$23.13; specifically, if it trades at any other price, an arbitrage opportunity is available. That example was
simplistic in that I assumed WBC paid no dividends during the next year.
Consider the stock TST which is currently trading at $10 and is expected to pay a dividend of $0.90 in exactly
five months’ time. The riskfree rate of interest is 6% pa.
A forward contract is written to deliver 1,000 TST shares in nine months’ time.
Required:
a) Calculate the no-arbitrage price of this forward contract.
b) Assume you have found someone willing to enter into a nine-month forward contract on TST at a delivery
price of $9.80. Explain what trades you would execute to capture the arbitrage opportunity.
c) Assume you have found someone willing to enter into a nine-month forward contract on TST at a delivery
price of $9. Explain what trades you would execute to capture the arbitrage opportunity.
Question 309
Today is the 1st of August. You are a financial officer for Goldtech, a US-based technology company. Goldtech
specialises in the manufacture of gold based alloys for electrical components. The company just won a tender with
a multinational computer hardware producer for the manufacture of gold based electrical components. Work is
expected to commence on the 1st of December this year.
The production manager is estimating that the company will require 2,000 ounces of gold in order to meet the
obligations underlying the contract. This quantity of gold must therefore be on hand when production starts in
December. The maximum amount the company can afford to spend on gold is $2m. Anything greater than this
and the tender will begin to be unprofitable.
At the spot price of gold is $850 per ounce, the tender is viable. However, you are concerned that the price per
ounce of gold will increase between now and the commencement of production. There are a number of courses of
action available to you and we will explore the outcomes of each.
a) Assume you do nothing. In December, the day before commencement of production, you purchase the gold
from the spot market a price of $1200 per ounce. How much will 2,000 ounces of gold cost you?
b) Rather than risking the adverse consequences of a gold price increase, we simply purchase 2,000 ounces of
gold today at a spot price of $850 per ounce place the gold in a storage facility and hold onto the gold until
production starts in December. Assume that there are no storage costs for the gold. How much does the gold
cost?
9
c) While you like the idea from part b of buying the gold today, you don’t have sufficient cash to be buying it
so far in advance of the production date. Instead, you borrow enough money from a bank to buy the gold
today. Assume that the borrowing cost is 8% pa. Again, assume zero storage costs. The effective cost of the
gold is the payout figure on the loan. How much is it?
d) Continuing on from part c, now assume that there is a storage cost for the gold. The bank that loans you the
cash also offers a secure vault to store your gold at a storage cost of 3% pa. What is the effective cost of gold
in this case?
e) Gold futures are traded on the New York Mercantile Exchange. Calculate the fair price for the delivery of
gold on 30 November. Assume that you use these gold futures to hedge the price risk. Will you go long or
short? What is the effective cost of the gold using the futures contracts?
f) If the quoted futures price for November delivery gold was in fact $900 per ounce, there is an arbitrage
opportunity available. Describe how to take advantage of this opportunity and quantify the profit for 2,000
ounces of gold.
10
Question 401
For each of the following option positions, calculate:
• The cashflow paid or received today on entering the position,
• Whether you want the price of the underlying share to go up or down,
• The breakeven share price for the position,
• Whether or not you will exercise the option,
• The gross payoff at expiry, and
• The net payoff at expiry.
a) You enter a long position in a call option. The strike price is $20 and the option premium is $0.35. At expiry,
the price of the underlying share is $15.
b) You enter a long position in a call option. The strike price is $20 and option premium is $0.35. At expiry, the
price of the underlying share is $18.
c) You enter a long position in a call option. The strike price is $20 and option premium is $0.35. At expiry, the
price of the underlying share is $20.20.
d) You enter a long position in a call option. The strike price is $20 and option premium is $0.35. At expiry, the
price of the underlying share is $20.35.
e) You enter a long position in a call option. The strike price is $20 and option premium is $0.35. At expiry, the
price of the underlying share is $21.
f) You enter a long position in a call option. The strike price is $20 and option premium is $0.35. At expiry, the
price of the underlying share is $21.50.
11
Question 402
For each of the following option positions, calculate:
• The cashflow paid or received today on entering the position,
• Whether you want the price of the underlying share to go up or down,
• The breakeven share price for the position,
• Whether or not you will exercise the option,
• The gross payoff at expiry, and
• The net payoff at expiry.
a) You enter a short position in a call option. The strike price is $20 and option premium is $0.35. At expiry,
the price of the underlying share is $15.
b) You enter a short position in a call option. The strike price is $20 and option premium is $0.35. At expiry,
the price of the underlying share is $18.
c) You enter a short position in a call option. The strike price is $20 and option premium is $0.35. At expiry,
the price of the underlying share is $20.20.
d) You enter a short position in a call option. The strike price is $20 and option premium is $0.35. At expiry,
the price of the underlying share is $20.35.
e) You enter a short position in a call option. The strike price is $20 and option premium is $0.35. At expiry,
the price of the underlying share is $21.
f) You enter a short position in a call option. The strike price is $20 and option premium is $0.35. At expiry,
the price of the underlying share is $21.50.
12
Question 403
For each of the following option positions, calculate:
• The cashflow paid or received today on entering the position,
• Whether you want the price of the underlying share to go up or down,
• The breakeven share price for the position,
• Whether or not you will exercise the option,
• The gross payoff at expiry, and
• The net payoff at expiry.
a) You enter a long position in a put option. The strike price is $5 and the option premium is $0.50. At expiry,
the price of the underlying share is $5.40.
b) You enter a long position in a put option. The strike price is $5 and option premium is $0.50. At expiry, the
price of the underlying share is $4.80.
c) You enter a long position in a put option. The strike price is $5 and option premium is $0.50. At expiry, the
price of the underlying share is $4.50.
d) You enter a long position in a put option. The strike price is $5 and option premium is $0.50. At expiry, the
price of the underlying share is $4.30.
e) You enter a long position in a put option. The strike price is $5 and option premium is $0.50. At expiry, the
price of the underlying share is $3.80.
Question 404
For each of the following option positions, calculate:
• The cashflow paid or received today on entering the position,
• Whether you want the price of the underlying share to go up or down,
• The breakeven share price for the position,
• Whether or not you will exercise the option,
• The gross payoff at expiry, and
• The net payoff at expiry.
a) You enter a short position in a put option. The strike price is $5 and the option premium is $0.50. At expiry,
the price of the underlying share is $5.40.
b) You enter a short position in a put option. The strike price is $5 and option premium is $0.50. At expiry, the
price of the underlying share is $4.80.
c) You enter a short position in a put option. The strike price is $5 and option premium is $0.50. At expiry, the
price of the underlying share is $4.50.
d) You enter a short position in a put option. The strike price is $5 and option premium is $0.50. At expiry, the
price of the underlying share is $4.30.
e) You enter a short position in a put option. The strike price is $5 and option premium is $0.50. At expiry, the
price of the underlying share is $3.80.
13
Question 405
As at 5 July 2017, QBE share price closed at $12.10. The extract below shows a range of call options available on
QBE Insurance. The “Last Sale” column indicates the price paid for the last sale of the option on the previous
day. As such, it provides an indication of what it would cost you to enter a long position (or what you would
receive if you entered a short position).
For each option series shown (i.e., for each row in the extract), indicate:
• Whether the call option is currently in the money, or out of the money, and
• What the breakeven point is.
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Question 406
As at 5 July 2017, TLS share price closed at $4.41. The extract below shows a range of put options available on
Telstra. The “Last Sale” column indicates the price paid for the last sale of the option on the previous day. As
such, it provides an indication of what it would cost you to enter a long position (or what you would receive if
you entered a short position).
For each option series shown (i.e., for each row in the extract), indicate:
• Whether the put option is currently in the money, or out of the money, and
• What the breakeven point is.
15
Question 501
A trader is interested in setting up a specialised strategy by investing in put options as
indicated in the following table. All these options are written on the same underlying share
and have the same maturity. Answer part (a), (b) and (c).
Exercise price Option premium
Long 1 put $50 $3
Short 1 put $60 $5
Short 1 put $67 $8
Long 1 put $77 $12
a) Draw the net profit and loss diagram for this strategy. Show the workings and mark the
intercepts on the X- and Y- axes clearly.
b) Work out the net profit or loss for each case in the table.
The share price at maturity is: The net profit or loss is:
$48.00
$51.50
$59.00
$65.00
$76.50
c) Explain the trader’s expectation of the future share price movement of the underlying share
by adopting this strategy.
Question 502
What is meant by a protective put? Draw the diagram for a protective put with all the options
and other positions that make up the protective put. What is the equivalent position in calls
that will give the same payoff as a protective put?
Question 601
A put option is available that will give you the right to sell a single share of ABC. The option
will expire in two months time and can be exercised at any time up to the expiry date. The
exercise price is set at $10.40 with the current ABC price at $10.00. The risk-free interest
rate is 12.0% per annum. The up factor for each step is 1.06 and the down factor is 0.944.
(a) Use a two period binomial model of share price movements to estimate the possible
future payoffs from the option at expiry. Each time interval in the binomial model is
to be of length one month. Draw the stock price lattice and the lattice of intrinsic
(immediate exercise) values. Hence derive the price for purchasing the option today.
(b) Hence derive the fair value for purchasing the option today.
(c) If the option could be bought today for $0.41 would you recommend buying the
option? Give reasons for your answer.
16
(d) Discuss the strengths, weaknesses and assumptions of the binomial option pricing
model.
Question 602
You observe the shares on ABC trading at $61.00. Call and put options on ABC shares are
also trading. Each option contract is written over 1000 shares. A three month call option at a
strike price of $60.00 is trading at $3.00 while the put option is trading at $1.08. Show that
there is an arbitrage profit to be made, and give explicit details of how the mispricing will be
arbitraged and what the profit (in dollars) of your arbitrage strategy will be. You must show
the exact strategy. Assume that the risk-free rate is 4.5% p.a. (continuously compounded).
Question 603
A stock price is currently $20.00. It is known that at the end of three months it will be either
$23 or $17. The risk-free rate of interest is 5% per annum with continuous compounding.
What is the value of a three month European put option with a strike price of $20. You must
use no-arbitrage (delta hedging) arguments to calculate a riskless portfolio in order to derive
the value of the put.
17
Key Figure Answers
The full solutions to these supplementary questions will be made available in due course. The optimal way to get
the most out of these questions is to keep working on them until you solve them! That’s where the value of these
revision questions lies. There is little value in having both questions and answers and just looking through them.
Question KeyFig Answer Question KerFig Answer
Q101 c
Q101 d
Loss 7830
Profit 10,490
501 Net profit/loss:
-2,-0.50,+7.00, +8.00,-
1.50
Q104a
Q104b
Profit EUR 6,000
Profit AUD 9,090
601 Price = $0.5066
At $0.41 option is
undervalued
Q105b
Q105c
Q105d
$25,250
$97,500
$25,250
602 Call is overpriced relative
to put.
Q202ci
Q202cii
Loss 2,000,000
Profit 1,750,000
Overall cost $10,750,000
603 Put price = $1.357
Q203a
Q203b
Q203c
850 contracts
HKD 686,040,000; 55.250m loss
HKD 576,276,000;
profit 51m
Q204 Cost is $25,000 in every case
Q205a
Q205b
Receive $145m
$35m loss, ovberall cost $145m
Q301a
Q301b
Q301c
F=$11.62
$0.62 arbitrage profit
$3.38 arbitrage profit
Q302a F=12,891
Q303d F=$32,661.51
Q304a
Q304b
Q304c
F=0.0694 or F=14.4118 (equivalent!)
Arbitrage profit HKD 7.48
Arbitrage profit HKD 6.93
Q305a
Q305b
Q305c
Q305d
F = $131.6217
F = $42.8155
F = $20.9786
F = $405,259,413
Q306 0.8354 or 1.1970 (equivalent!)
Q307b
Q307c
Q307d
Q307e
Borrow AUD 16,500.88; owe AUD
16,792.19
F = 0.5955
Arbitrage profit $1,390
Arbitrage profit $3,459
Q308a
Q308b
Q308c
F = $9.54
Arbitrage profit $0.26
Arbitrage profit $0.54
Q309a
Q309b
Q309c
Q309d
Q309e
Q309f
$2.4m
$1.7m
$1,745,943
$1,763,490
$1,763,490
arbitrage profit $36,510
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学霸联盟
