Semester One 2022
Exam - Alternative Assessment Task
STUDENT ID:
SURNAME:
GIVEN NAME:
UNIT CODE:
BFF5340
UNIT TITLE:
APPLIED DERIVATIVES
ASSESSMENT DURATION:
2 hours 30 minutes (includes reading,
downloading, and uploading time)
 This is an individual assessment task.
 All responses must be included within this document and under
individual questions.
 Students are required to answer ALL questions.
 This assessment accounts for 60% of the total in the unit and has a hurdle
requirement of 45% to pass the unit.
 Some questions require to be answered in Excel. All this Excel work is to
be completed in 1 single Excel file (with different worksheets).
 Upon completion of this assessment task, please upload this Word
document, together with the Excel file, to Moodle using the assignment
submission link. The total number of files to upload is 2.
 Your submission must occur within 2 hours 30 minutes of the official
commencement of this assessment task (Australian Eastern Standard
Time).
Please read the next page carefully and sign and date the Student
Statement before commencing the assessment task.
Page 1 of 10
Intentional plagiarism or collusion amounts to cheating under Part 7 of the Monash
University (Council) Regulations
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expressing them and passing them off as one’s own. For example, by failing to give
appropriate acknowledgment. The material used can be from any source (staff, students or
the internet, published and unpublished works).
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written, oral or practical work and includes paying another person to complete all or part of
the work.
Where there are reasonable grounds for believing that intentional plagiarism or collusion has
occurred, this will be reported to the Associate Dean (Education) or delegate, who may
disallow the work concerned by prohibiting assessment or refer the matter to the Faculty
Discipline Panel for a hearing.
Student Statement:
 I have read the university’s Student Academic Integrity Policy and Procedures.
 I understand the consequences of engaging in plagiarism and collusion as described in
Part 7 of the Monash University (Council) Regulations
https://www.monash.edu/legal/legislation/current-statute-regulations-and-relatedresolutionshttp://adm.monash.edu/legal/legislation/statutes
 I have taken proper care to safeguard this work and made all reasonable efforts to ensure
it could not be copied.
 I have not used any unauthorised materials in the completion of this assessment task.
 No part of this assessment has been previously submitted as part of another unit/course.
 I acknowledge and agree that the assessor of this assessment task may for the purposes
of assessment, reproduce the assessment and:
i. provide to another member of faculty and any external marker; and/or
ii. submit it to a text-matching software; and/or
iii. submit it to a text-matching software which may then retain a copy of the
assessment on its database for the purpose of future plagiarism checking.
 I certify that I have not plagiarised the work of others or participated in unauthorised
collaboration when preparing this assessment.
Signature:
(Type your full name)
Date:
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Page 2 of 10
Question
Allocated Marks
MARKS ALLOCATED TO QUESTIONS WITHIN THIS ASSESSMENT TASK
1
2
3
4
5
20
20
20
20
20
Office Use Only
TOTAL
100
Mark received
Second marking
Question 1
For each of the FOUR (4) statements below, state whether it is TRUE or FALSE (2 marks),
and EXPLAIN the reason (3 marks).
1) Ito’s Lemma shows that an increase in the price of an underlying stock, holding all else
constant, will cause a linear increase in the price of the call option of this underlying stock.
TRUE. This is true because the value of puts and calls are known to be affected by the
changes experienced in the underlying stock prices in a manner that sis relatively
straightforward. This relatively straightforward manner implies that when the stock prices
increase, the calls also gain value based on the fact that one has the ability to purchase the
asset underlying at prices lower than the market prices thus resulting to a decline in puts.
2) The option for management to delay investment in a project is akin to a European call
option.
FALSE. This is because the option to delay is taken when the firm has exclusive rights to a
project in a manner that it can delay taking the project to take it on a day that the project
becomes good when taken today while the Eurpoean call option grants the rights to acquire
the underlying security at expiry to the owner and in this case, the stock has to be trading
high above the strike price for it to be profitable to the investor when taken from call option.
3) The price of a receiver swaption is equal to the value of a European call option on a fixed
rate bond where the face value of the bond is the strike price.
TRUE. In the case of the European Call option, the settlement price is usually the official
closing price that operates for the expiration period in question and thus establishes the
options that are in the money and subjects them to auto-exercise, similar to receiver swaption
where the purchaser is allowed to choose to enter into a swap contract that provides the
option for them to be in receipt of fixed rates. It allows them to pay floating rates.
Page 3 of 10
4) A speculator has bought a 5-year single-name Credit Default Swap (CDS) on a reference
entity in which the speculator is the party paying the periodic spread. Since buying the
CDS, the creditworthiness of the reference entity has improved, and the likelihood of
default by the reference entity has decreased. The speculator will therefore make a markto-market gain on the CDS.
TRUE. This is because the Credit Default Swap operates by allowing the buyer to shift some
or all the risk to the other CGS seller or an insurance company for a consideration which is
the fee and thus the buyer receives credit protection and on the other end, the seller ends up
being guaranteed of the creditworthiness of the seccuirty.
(4× 5 = 20 marks)
Question 2
Consider a 2-year CDS on a corporate reference entity that has a hazard rate of 2.5% per annum
in the first year and 3% per annum in the second year. The risk-free rate is flat at 4% per annum
continuously compounded and the premium payments are made quarterly. If default occurs,
assume it happens midway through a payment period.
a) What is the probability of the reference entity defaulting at any time during the life of
the CDS?
−𝑺 × 𝒕
)
𝟏−𝑹
−𝟐. 𝟓% × 𝟏
𝑷(𝟎, 𝒕) = 𝟏 − 𝒆𝒙𝒑(
)
𝟏 − 𝟒%
𝑷(𝟎, 𝒕) = 𝟏 − 𝒆𝒙𝒑(
= 𝟏 − 𝒆𝒙𝒑(−𝟎. 𝟎𝟐𝟔𝟎𝟒)
= 𝟏 − 𝟎. 𝟗𝟕𝟒𝟑
= 𝟎. 𝟎𝟐𝟓𝟕
b) Compute the price of the CDS assuming the recovery rate is 45%.
Page 4 of 10
c) Compute the price of an equivalent binary CDS and explain why this might be more
attractive to a hedger and speculator than a regular CDS.
= 𝟏𝟎𝟓𝟓𝟕. 𝟓(𝟒% × 𝟏𝟎𝟎𝟎𝟎)
= 𝟒, 𝟐𝟐𝟑, 𝟎𝟎𝟎
This might be more attractive to a hedger and speculator than a regulator CDSbecause there
seems to be an offer for protection against any form of undesired price fluctuations as well
as the holding of a net position for gain.
(5 + 10 + 5= 20 marks)
Question 3
A fund manager buys a 3-month option to buy a 12-month put on the S&P 500 index that has
a strike of 4000. The 3-month option has a strike price of $100. Assume that the current level
of the S&P 500 index is 4000, the risk‐free rate is 3% per annum, the dividend yield on the
index is 2% per annum, and the volatility of the index is 20%. All rates are continuously
compounded.
a) Price the underlying put option using a binomial tree with 4 (four) steps.
b) Price the compound call option using the same tree.
Page 5 of 10
c) Explain why the fund manager may prefer to purchase a compound option for hedging
risk instead of buying a regular option.
Because hedge funds are highly flexible which is mainly attributed to the fact that their
nature allows them to be highly flexible more so on matters related to he investor terms and
investing provisions.
(10 + 6 + 4= 20 marks)
Question 4
A trader has a position that is long a 6-month European call option bought on a non-dividend
paying stock. The current stock price is $50 and the strike price is $45 per share. The volatility
of the stock is 20% per annum and the risk-free rate is 5% continuously compounded. The size
of the option contract is 100 shares.
a) If the stock price decreases by 10% in one day, what is the approximate 1-day loss for
the trader using the option’s delta to approximate the change in value?
Answer this question in Excel and name the worksheet VaR, or type or insert a screenshot
of your answer here.
b) Compute the 95% confidence, 10-day Value-at-Risk at of the trader’s position (i.e. 10day VaR(95)) using your answer from a). Assume there are 252 trading days in a year.
Page 6 of 10
Answer this question in Excel in the same worksheet VaR, or type or insert a screenshot of
your answer here.
c) Do you consider the linear approximation method as an accurate measure of the
maximum loss that the trader may suffer over 10 days? Explain your answer.
Type your answer here.
(6+8+6=20 marks)
Question 5
A company plans to invest $10 million in a floating rate note (FRN) paying LIBOR per annum
payable every 6 months for 5 years. It wishes to insure against a fall in interest rates so that it
is guaranteed to earn a minimum interest rate of 5% per annum for the life of the investment.
a) Describe a derivative that could be used to hedge the FRN and describe the expected
payoff at the end of each interest rate reset period.
Type your answer here.
b) Can the Black-Scholes-Merton (BSM) be used to price an interest rate option? Explain
your answer and identify any suitable alternative models.
Type your answer here.
c)
Price the floorlet that commences in 2 years. Assume that the forward 2-year LIBOR
rate is 6% per annum, with a volatility of 20% per annum. The risk-free rate for 2.5
years is 4% per annum continuously compounded.
Answer this question in Excel and name the worksheet as Floor, or type or insert a
screenshot of your answer here.
(6+6+8=20 marks)
Page 7 of 10
END OF ASSESSMENT
Page 8 of 10
Formulae Sheet
When stock price follows GBM, 𝑆(𝑇) = 𝑆(0)𝑒𝑥𝑝 [(𝜇 −
1
CRR binomial tree parameters: 𝑢 = 𝑒 𝜎√∆𝑡 ; 𝑑 = 𝑢 ; 𝑞 =
𝜎2
2
) 𝑇 + 𝜎𝜖√𝑇]
𝑒 (𝑟−𝑞)∆𝑡 −𝑑
𝑢−𝑑
Black-Scholes-Merton formula for European options on dividend-paying stocks
𝑐 = 𝑆𝑒 −𝑞𝑇 𝑁(𝑑1 ) − 𝑒 −𝑟𝑇 𝐾𝑁(𝑑2 )
𝑑1 =
𝑝 = 𝑒 −𝑟𝑇 𝐾𝑁(−𝑑2 ) − 𝑆𝑒 −𝑞𝑇 𝑁(−𝑑1 )
𝑆
𝜎2
ln (𝐾 ) + (𝑟 − 𝑞 + 2 ) 𝑇
𝑑2 = 𝑑1 − 𝜎√𝑇 =
𝜎√𝑇
𝑆
𝜎2
ln (𝐾 ) + (𝑟 − 𝑞 − 2 ) 𝑇
𝜎√𝑇
Black’s model on European futures options
𝑐 = 𝑒 −𝑟𝑇 [𝐹 𝑁(𝑑1 ) − 𝐾𝑁(𝑑2 )]
𝑑1 =
𝑝 = 𝑒 −𝑟𝑇 [𝐾𝑁(−𝑑2 ) − 𝐹𝑁(−𝑑1 )]
𝐹
𝜎2
ln (𝐾 ) + ( 2 ) 𝑇
𝑑2 = 𝑑1 − 𝜎√𝑇 =
𝜎√𝑇
𝐹
𝜎2
ln (𝐾 ) − ( 2 ) 𝑇
𝜎√𝑇
Black’s model on European bond options
𝑐 = 𝑃(0, 𝑇)[𝐹𝐵 𝑁(𝑑1 ) − 𝐾𝑁(𝑑2 )]
𝑑1 =
𝑝 = 𝑃(0, 𝑇)[𝐾𝑁(−𝑑2 ) − 𝐹𝐵 𝑁(−𝑑1 )]
𝜎2
𝐹
ln ( 𝐾𝐵 ) + ( 2𝐵 ) 𝑇
𝑑2 = 𝑑1 − 𝜎√𝑇 =
𝜎𝐵 √𝑇
𝜎2
𝐹
ln ( 𝐾𝐵 ) − ( 2𝐵 ) 𝑇
𝜎𝐵 √𝑇
𝑐𝑎𝑝𝑙𝑒𝑡 = 𝐿𝛿𝑘 𝑃(0, 𝑡𝑘+1 )[𝐹𝑘 𝑁(𝑑1 ) − 𝑅𝐾 𝑁(𝑑2 )]
𝑓𝑙𝑜𝑜𝑟𝑙𝑒𝑡 = 𝐿𝛿𝑘 𝑃(0, 𝑡𝑘+1 )[𝑅𝐾 𝑁(−𝑑2 ) − 𝐹𝑘 𝑁(−𝑑1 )]
𝑑1 =
𝜎2
𝐹
ln (𝑅𝑘 ) + ( 2𝑘 ) 𝑡𝑘
𝐾
𝜎𝑘 √𝑡𝑘
𝑛
2
𝜎∆𝑃
=
∑ 𝛼𝑖2 𝜎𝑖2
𝑖=1
∆𝑃 ≈ ∑𝑖 𝑆𝑖 𝛿𝑖 ∆𝑥𝑖
𝑑2 = 𝑑1 − 𝜎√𝑇 =
𝜎2
𝐹
ln (𝑅𝑘 ) − ( 2𝑘 ) 𝑡𝑘
𝐾
𝜎𝑘 √𝑡𝑘
𝑛−1
+ 2 ∑ ∑ 𝜌𝑖𝑗𝛼𝑖 𝛼𝑗 𝜎𝑖 𝜎𝑗
𝑖=1 𝑗>𝑖
1
∆𝑃 ≈ 𝑆𝛿𝑟 + 2 𝑆 2 𝛾𝑟 2
99%, 𝑁 − 𝑑𝑎𝑦 𝑉𝑎𝑅 = 2.33√𝑁𝜎∆𝑃 ; 95%, 𝑁 − 𝑑𝑎𝑦 𝑉𝑎𝑅 = 1.64√𝑁𝜎∆𝑃
̅
Probability of survival tile end of time t: 𝑉(𝑡) = 𝑒 −𝜆𝑡
̅
Probability of default at some time between now and time t: 𝑄(𝑡) = 1 − 𝑒 −𝜆𝑡
Probability of default over future period [t1, t2] as seen today: 𝑄(𝑡2 ) − 𝑄(𝑡1 ) = 𝑉(𝑡1 ) −
𝑉(𝑡2 )
Page 9 of 10
Table for N x  when x  0 .
x
0.0
0.1
0.2
0.3
0.4
0.5
0.00
0.5000
0.5398
0.5793
0.6179
0.6554
0.6915
0.01
0.5040
0.5438
0.5832
0.6217
0.6591
0.6950
0.02
0.5080
0.5478
0.5871
0.6255
0.6628
0.6985
0.03
0.5120
0.5517
0.5910
0.6293
0.6664
0.7019
0.04
0.5160
0.5557
0.5948
0.6331
0.6700
0.7054
0.05
0.5199
0.5596
0.5987
0.6368
0.6736
0.7088
0.06
0.5239
0.5636
0.6026
0.6406
0.6772
0.7123
0.07
0.5279
0.5675
0.6064
0.6443
0.6808
0.7157
0.08
0.5319
0.5714
0.6103
0.6480
0.6844
0.7190
0.09
0.5359
0.5753
0.6141
0.6517
0.6879
0.7224
0.6
0.7
0.8
0.9
1.0
0.7257
0.7580
0.7881
0.8159
0.8413
0.7291
0.7611
0.7910
0.8186
0.8438
0.7324
0.7642
0.7939
0.8212
0.8461
0.7357
0.7673
0.7967
0.8238
0.8485
0.7389
0.7704
0.7995
0.8264
0.8508
0.7422
0.7734
0.8023
0.8289
0.8531
0.7454
0.7764
0.8051
0.8315
0.8554
0.7486
0.7794
0.8078
0.8340
0.8577
0.7517
0.7823
0.8106
0.8365
0.8599
0.7549
0.7852
0.8133
0.8389
0.8621
1.1
1.2
1.3
1.4
1.5
0.8643
0.8849
0.9032
0.9192
0.9332
0.8665
0.8869
0.9049
0.9207
0.9345
0.8686
0.8888
0.9066
0.9222
0.9357
0.8708
0.8907
0.9082
0.9236
0.9370
0.8729
0.8925
0.9099
0.9251
0.9382
0.8749
0.8944
0.9115
0.9265
0.9394
0.8770
0.8962
0.9131
0.9279
0.9406
0.8790
0.8980
0.9147
0.9292
0.9418
0.8810
0.8997
0.9162
0.9306
0.9429
0.8830
0.9015
0.9177
0.9319
0.9441
1.6
1.7
1.8
1.9
2.0
0.9452
0.9554
0.9641
0.9713
0.9772
0.9463
0.9564
0.9649
0.9719
0.9778
0.9474
0.9573
0.9656
0.9726
0.9783
0.9484
0.9582
0.9664
0.9732
0.9788
0.9495
0.9591
0.9671
0.9738
0.9793
0.9505
0.9599
0.9678
0.9744
0.9798
0.9515
0.9608
0.9686
0.9750
0.9803
0.9525
0.9616
0.9693
0.9756
0.9808
0.9535
0.9625
0.9699
0.9761
0.9812
0.9545
0.9633
0.9706
0.9767
0.9817
2.1
2.2
2.3
2.4
2.5
0.9821
0.9861
0.9893
0.9918
0.9938
0.9826
0.9864
0.9896
0.9920
0.9940
0.9830
0.9868
0.9898
0.9922
0.9941
0.9834
0.9871
0.9901
0.9925
0.9943
0.9838
0.9875
0.9904
0.9927
0.9945
0.9842
0.9878
0.9906
0.9929
0.9946
0.9846
0.9881
0.9909
0.9931
0.9948
0.9850
0.9884
0.9911
0.9932
0.9949
0.9854
0.9887
0.9913
0.9934
0.9951
0.9857
0.9890
0.9916
0.9936
0.9952
2.6
2.7
2.8
2.9
3.0
0.9953
0.9965
0.9974
0.9981
0.9987
0.9955
0.9966
0.9975
0.9982
0.9987
0.9956
0.9967
0.9976
0.9982
0.9987
0.9957
0.9968
0.9977
0.9983
0.9988
0.9959
0.9969
0.9977
0.9984
0.9988
0.9960
0.9970
0.9978
0.9984
0.9989
0.9961
0.9971
0.9979
0.9985
0.9989
0.9962
0.9972
0.9979
0.9985
0.9989
0.9963
0.9973
0.9980
0.9986
0.9990
0.9964
0.9974
0.9981
0.9986
0.9990
3.1
3.2
3.3
3.4
3.5
0.9990
0.9993
0.9995
0.9997
0.9998
0.9991
0.9993
0.9995
0.9997
0.9998
0.9991
0.9994
0.9995
0.9997
0.9998
0.9991
0.9994
0.9996
0.9997
0.9998
0.9992
0.9994
0.9996
0.9997
0.9998
0.9992
0.9994
0.9996
0.9997
0.9998
0.9992
0.9994
0.9996
0.9997
0.9998
0.9992
0.9995
0.9996
0.9997
0.9998
0.9993
0.9995
0.9996
0.9997
0.9998
0.9993
0.9995
0.9997
0.9998
0.9998
3.6
3.7
3.8
3.9
4.0
0.9998
0.9999
0.9999
1.0000
1.0000
0.9998
0.9999
0.9999
1.0000
1.0000
0.9999
0.9999
0.9999
1.0000
1.0000
0.9999
0.9999
0.9999
1.0000
1.0000
0.9999
0.9999
0.9999
1.0000
1.0000
0.9999
0.9999
0.9999
1.0000
1.0000
0.9999
0.9999
0.9999
1.0000
1.0000
0.9999
0.9999
0.9999
1.0000
1.0000
0.9999
0.9999
0.9999
1.0000
1.0000
0.9999
0.9999
0.9999
1.0000
1.0000
Page 10 of 10