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Excel代写-MSIN0107

时间：2021-03-01

Assessment Information Coursework 2020-21

Module name: MSIN0107

Module code: Advanced Quantitative Finance

Module leader name: Ming Yang

Academic year: INSERT

Term 1, 2 or 3: INSERT

Type of assessment: Coursework assignment

Nature of assessment – group:

Content of this Assessment Brief

Section Content

A Core information

B Coursework Brief and Requirements

C Module learning outcomes covered in this

assessment

D Assessment criteria

E Groupwork instructions (if applicable)

F Additional information from module leader (if

applicable)

Page 2 of 9

Section A: Core information

This assessment is

marked out of:

100

% weighting of this

assessment within total

module mark

10%

Word count/number of

pages - maximum

1,000 words

There is no penalty for using fewer words pages.

Determining word count

impacted by Turnitin

• After submission to Turnitin, the Turnitin recorded word

count is usually higher than the word count in a Word

document.

• Where the assessment brief specifies a maximum word

count, on the front cover of your submission record the

number of words as recorded in your Word document.

• It is the Word document word count which will be taken

account of in marking, NOT the Turnitin word count.

Footnotes, appendices,

tables, figures, diagrams,

charts included

in/excluded from word

count/page length?

Any footnotes, appendices are not included in page limit.

Bibliographies, reference

lists included

in/excluded from word

count?

Title page, table of contents, any bibliography are excluded from the

page limit.

Penalty for exceeding

specified word

count/page length?

• Where there is a specified word count/page length and this is

exceeded, yes there is a penalty: 10 percentage points

deduction, capped at 40% for Levels 4,5, 6, and 50% for Level

7. Refer to Academic Manual Section 3: Module Assessment -

3.13 Word Counts.

• Where there is no specified word count/page length no

penalty applies.

Requirements for/use of

references

• Where you draw upon sources you must cite them

appropriately.

• As appropriate, you may draw upon a range of sources

including, illustratively, journal articles, other textbooks,

industry reports.

• As appropriate, you may draw upon course materials –

lecture slides, notes, handouts, readings, textbook(s) - you

engaged with in your studying of this module.

• Unless citing content specifically (e.g. a quote from a book)

you should not be copying word for word from lecture slides,

notes, handouts, readings, textbook(s).

• You should capture, articulate and communicate your views,

thoughts and learning in your own words.

• If you do provide quotes from any lecture slides, notes,

handouts, readings, textbook(s) you should cite them and

provide references in the usual way.

Page 3 of 9

• Be aware that a number of academic misconduct checks,

including the use of Turnitin, are available to your module

leader.

• If required/where appropriate UCL Academic Misconduct

penalties may be applied (see immediately below).

Academic misconduct

(including plagiarism)

• Academic integrity is paramount.

• It is expected that your submission and content will be your

own work with no academic misconduct.

• Academic Misconduct is defined as any action or attempted

action, including collusion with other students, that may

result in a student obtaining an unfair academic

advantage. There are severe penalties for Academic

Misconduct, including, where appropriate and required,

exclusion from UCL.

• Refer to Academic Manual Section 9: Student Academic

Misconduct Procedure - 9.2 Definitions.

Submission date 4th March 2021

Submission time 10am UK time

Penalty for late

submission?

Yes. Standard UCL penalties apply. Students should refer to

https://www.ucl.ac.uk/academic-manual/chapters/chapter-4-

assessment-framework-taught-programmes/section-3-module-

assessment#3.12

Submitting your

assignment

The assignment MUST be submitted to the module submission link

located within this module’s Moodle ‘Submissions’ tab by the

specified deadline.

Anonymity of identity.

Normally, all submissions

are anonymous unless

the nature of the

submission is such that

anonymity is not

appropriate, illustratively

as in presentations or

where minutes of group

meetings are required as

part of a group work

submission

Anonymity is required.

Your name should NOT appear anywhere on your submission.

Return and status of

marked assignments

• At the latest this will be within 4 weeks from the date

of submission as per UCL guidelines, but we will

endeavour to return it earlier than this.

• Assessments are subject to appropriate double

marking/scrutiny, and internal quality inspection by

a nominated School of Management internal

assessor. All results when first published are

provisional until confirmed by the relevant External

Examiner and the Examination Board.

Page 4 of 9

• No appeals regarding your published mark are

available until after confirmation by that

Examination Board. UCL regulations specify that

academic judgment applied within the marking

process cannot be challenged.

Uploading your submission

• Unless specifically instructed otherwise in the assessment document, please upload your work as a

single file via the submission link on Moodle.

o Wherever possible you should type/use Excel (as appropriate) for your answers and follow

instructions later in this assessment document.

o If you do have to include any elements that are not typed/computer generated (e.g. figures,

diagrams, equations etc.) as instructed by your module leader, please follow the advice for

submitting handwritten answers for any submission that requires scanning documents. (The

webpage refers to 24-hour timed exams but is applicable to this assessment).

o If you are unable to type your answers for medical reasons, please contact Student Support

and Wellbeing to arrange a SORA and notify your programme administrator.

o If for any reason you are not able to use the app recommended by ISD at the link above, you

can consult the following resources for advice about preparing your submission:

Submitting handwritten assignments to Moodle using mobile or tablet Devices -

Device Camera

Submitting handwritten assignments to Moodle using mobile or tablet devices - MS

One Drive App

• Please DOUBLE CHECK that the file you are uploading is the correct one and is complete (with all

pages visible). You should only submit your final version of the work to the submission box. Once the

original deadline has passed, any submission made to the official submission box will be taken as

the final submission. Work submitted after the original submission deadline will NOT be removed

and a new version cannot be submitted. If you wish to check your work before submitting your final

version, you can use the Turnitin Drafts Checker rather than your official submission inbox. Please be

sure that the version of the assignment you submit is the version you intend to be marked for that

module. If you are granted ECs in relation to a piece of work already submitted, the mitigation

applied will be a deferral and not an extension. If you are unable to submit on time, you may submit

an EC form to request an extension if you have legitimate mitigating circumstances.

Page 5 of 9

Technical Problems

If you encounter difficulties submitting your assessment via Moodle, then please immediately notify (by

email) your department (Programme Administrators ONLY), explaining the problem and including a copy of

the work you are trying to submit. ONLY use this approach if you can show that you have tried to download

from/upload to Moodle and encountered technical difficulties.

Advice and other support

• Student Support and Wellbeing

Page 6 of 9

Section B: Coursework Brief and Requirements

See document at the end of the brief.

Page 7 of 9

Section C: Module Learning Outcomes covered in this

Assessment

This assignment contributes towards the achievement of the module Learning

Outcomes as specified in the module description.

Page 8 of 9

Section D: Assessment criteria

Within each section of this coursework you may be assessed on the following aspects, as

applicable and appropriate to this particular assessment, and should thus consider these aspects

when fulfilling the requirements of each section:

• The accuracy of any calculations;

• The strengths and quality of your overall analysis and evaluation;

• Appropriate use of relevant theoretical models, concepts and frameworks;

• The rationale and evidence that you provide in support of your arguments;

• The credibility and viability of the evidenced conclusions/recommendations/plans of

action you put forward;

• Structure and coherence of your considerations and reports;

• As and where required, relevant and appropriate, any references should use either

the Harvard OR Vancouver referencing system (see References, Citations and

Avoiding Plagiarism)

• Academic judgement regarding the blend of scope, thrust and communication of

ideas, contentions, evidence, knowledge, arguments, conclusions.

• Each part has requirements with allocated marks, maximum word count limits/page

limits and where applicable, templates that are required to be used.

You are advised to refer to the UCL Assessment Criteria Guidelines, located at

https://www.ucl.ac.uk/teaching-learning/sites/teaching-learning/files/migrated-

files/UCL_Assessment_Criteria_Guide.pdf

Page 9 of 9

Section E: Groupwork Instructions

This is a team assignment. Each team should submit a pdf version report in Moodle. The

report should contain your answers/arguments and will be graded. Please also prepare

Powerpoint slides that summarize your findings. You don't have to submit the Powerpoint

slides in Moodle. In class, I may randomly select one or two teams to present their

Powerpoint slides.

This assignment is due at 10am on 4th March, 2021. See the assignment instructions here

and data here.

You'll need to use the Black-Scholes formula to calculate option prices and implied volatility.

To make your life easy, here I provide two useful Excel add-ins: optall3.xla and

optbasic3.xla. Please put the add-ins to "C:\Program Files\Microsoft Office\Office16\Library"

and then install the two add-ins. To install the add-ins, open any Excel spreadsheet --> file -

-> options --> add-ins --> choose "Excel add-ins" in the bottom box and click "go" -->

browse and choose the two add-ins at the path where you put them --> click "ok".

These add-ins are provided in a CD published with the "McDonald" textbook (Derivatives

Markets, Third Edition, Robert L. McDonald, Addison Wesley, Copyright 2013) and are thus

intended for educational, non-commercial use. Neither the author nor publisher represent

these spreadsheets as suitable for any purpose other than to help you learn the material in

the text.

Section F: Additional information from module leader(s)

N/A

MSIN0107: Advanced Quantitative Finance

UCL School of Management

Prof. Yang

m-yang@ucl.ac.uk

Group Course Work 2

I Introduction and Instructions

Please read the HBS case 9-201-071 Pine Street Capital carefully, and answer the

following questions.

A Black-Scholes Functions

Youll need to use the Black-Scholes formula to calculate option prices and implied

volatility. To make your life easy, here I provide two useful Excel add-ins:1 op-

tall3.xla and optbasic3.xla. Please put the add-ins to "C:nProgram FilesnMicrosoft

O¢ cenO¢ ce16nLibrary" or "C:nProgram Files (x86)nMicrosoft O¢ cenrootnO¢ ce16nLibrary"

and then install the two add-ins. To install the add-ins, open any Excel spreadsheet

> le > options > add-ins > choose "Excel add-ins" in the bottom box and click

"go" > browse and choose the two add-ins at the path where you put them > click

"ok".

Once the add-ins are installed, you should be able to use the Excel functions in the

table below. (You may just need to use a few of them, e.g., BSCallImpVol, BSPut,

BSPutDelta, etc. You may want to play with others so I include all the functions here

FYI.) The following symbol de nitions are used in these functions: s= stock price,

k= strike price, v= volatility (annualized), r= interest rate (continuously-

compounded, annualized), t= time to expiration (years), and d= dividend yield

(continuously-compounded, annualized).

1These add-ins are provided in a CD published with the "McDonald" textbook (Derivatives Mar-

kets, Third Edition, Robert L. McDonald, Addison Wesley, Copyright 2013) and are thus intended

for educational, non-commercial use. Neither the author nor publisher represent these spreadsheets

as suitable for any purpose other than to help you learn the material in the text.

1

Function De nition Function Description

BSCall(s, k, v, r, t, d) European call option price

BSPut(s, k, v, r, t, d) European put option price

BSCallDelta(s, k, v, r, t, d) European call delta

BSPutDelta(s, k, v, r, t, d) European put delta

BSCallGamma(s, k, v, r, t, d) European call gamma

BSPutGamma(s, k, v, r, t, d) European put gamma

BSCallVega(s, k, v, r, t, d) European call vega

BSPutVega(s, k, v, r, t, d) European put vega

BSCallRho(s, k, v, r, t, d) European call rho

BSPutRho(s, k, v, r, t, d) European put rho

BSCallTheta(s, k, v, r, t, d) European call theta

BSPutTheta(s, k, v, r, t, d) European put theta

BSCallPsi(s, k, v, r, t, d) European call psi

BSPutPsi(s, k, v, r, t, d) European put psi

BSCallElast(s, k, v, r, t, d) European call elasticity

BSPutElast(s, k, v, r, t, d) European put elasticity

BSCallImpVol(s, k, v, r, t, d, c) Implied volatility for European call2

BSPutImpVol(s, k, v, r, t, d, c) Implied volatility for European put3

BSCallImpS(s, k, v, r, t, d, c) Implied stock price for a given European call option price

BSPutImpS(s, k, v, r, t, d, c) Implied stock price for a given European put option price

II Case Summary

Pine Street Capital (PSC) is a technology hedge fund located in San Francisco, Cali-

fornia. PSC manages a fund that invests primarily in semiconductor companies that

produce integrated circuits for broadband communications including wide and local

area networks, optical components, and storage area networks. It is currently July,

2000 in the case, and the NASDAQ market (where most of the stocks that PSC invests

in are traded) index reached a peak of over 5,000 a few months ago but has dropped

2The option price is entered as c; the volatility entered does not matter.

3The option price is entered as c; the volatility entered does not matter.

2

considerably since then. In addition, the NASDAQ has experienced a historically un-

precedented amount of volatility over the last several months, as shown in Exhibit 7

of the case. Due to the market drop and volatility, PSCs fund has experienced con-

siderable problems in the last few months. Even though the fund has had a policy

of hedging market risk, the fund has nevertheless experienced large losses on many

days (sometimes on several consecutive days) in the last few months. This has created

problems for the fund because of the leverage employed by the fund. Some of the

losses that the fund had experienced had been large enough that the fund had come

dangerously close to having its prime broker, a prominent Wall Street rm, liquidate

the fund. Harold Yoon, a partner in the fund, now must evaluate the funds market

hedging program over the last few months to determine why the fund had experienced

such large losses on many days.

III Derivatives and Leverage

Consider the following binomial tree of the price movement of a non-dividend-paying

stock, assume the time period is one year (i.e., h = 1), and the e¤ective one-year

interest rate is 20% (i.e., er1 = 1 + 20%).

% Su = 140

S0 = 100

& Sd = 90

1. [2 points] Please calculate u and d, the gross returns on the stock for both states

of the world.

2. [5 points] Consider an at-the-money European call option with maturity of 1

year. Compute the and B of the call option. What is the gross return on a

long position in the call option (You need calculate the return on the call option

at both nodes, u and d)?

3. [3 points] Is the call option riskier than the stock? Why? Sometimes we say a

call option is like a leveraged position on the underlying stock, comment on this.

3

4. [3 points] Consider a futures contract on one share of the stock. What is the

no-arbitrage futures price (i.e., the forward price), F0;T?

5. [5 points] Assume an initial margin requirement of 8:33% of the futures price,

F0;T . What is the return on a long position in the futures contract? (Again, the

realized return will depend on the state of the world. Also, note that balances on

the margin account will earn risk-free return.) What is the expected return on

the futures contract under the risk-neutral probability? Is the futures contract

riskier than the stock?

6. [7 points] Can you invest in stocks and a risk-free bond to replicate the payo¤

of the futures contact, how? (You need to take into account that investing in

the futures contract involves an initial investment in the margins account.) Is

the futures contract in the above example a leveraged position in the underlying

stock?

IV Hedging with Put Options

1. [5 points] Use the historical data on NASDAQ 100 index in the Excel le NAS-

DAQ Index_PSC.xlsx 4 to estimate the volatility of the NASDAQ 100 index

during the sample period.

Hint: You need to rst get the data series for ln

St+1

St

, and estimate the stan-

dard deviation of the log return process (Recall that we assume the log return

process is i.i.d. normal). Since you are using monthly data, you need to trans-

form the monthly estimate into annual volatility. You can do so by using the

following formula:

Annual = Monthly

p

12

2. [5 points] Suppose on Sep 30, 2018, an at-the-money European call option on

the NASDAQ 100 index with maturity of 1 year is traded at $425.7661. Assume

the continuously compounded LIBOR is 3% per annum, and the continuously

4This can be downloaded from the course website.

4

compounded dividend yield is 0%. What is the implied volatility of the NASDAQ

100 index (from the Black-Scholes model)?

3. [5 points] Please nd the data for the NASDAQ 100 index during Sep and

Oct 2017 in the spread sheet named "Oct 2017" in the Excel le NASDAQ In-

dex_PSC.xlsx. Consider an at-the-money European put option on one NASDAQ

100 index on Sep 21, 2017. The maturity of the option is one year (the option

expires on Sep 21, 2018, i.e. the third Friday of September, 2018. Take 1 year as

252 trading days, and each trading day as 1/252 year). Calculate the theoretical

Black-Scholes prices of this put option for each day in the spreadsheet Oct 2017

and ll in the column "BS Put Price". Please use the continuously compounded

annual interest of 3% per year. Please use the implied volatility you obtained in

part 2 when calculating the Black-Scholes prices.

4. [5 points] Suppose you invested 1 million US dollar in the NASDAQ 100 index 5 6

on Sep 21, 2017. Suppose you want to use the above put option on NASDAQ 100

index (That is, the at-the-money put option on the index with one year maturity

described in the last question) to hedge the risks of your investment. To construct

a neutral position, how many put option contracts do you need to purchase

on Sep 21, 2017? (Note that each put option contract on the index contains 100

put options on the index. Assume you can take fractions of an option contract.)

5. [5 points] Suppose you rebalance your position in the put option everyday to

5Of course, trading the NASDAQ 100 index directly can be very costly. In practice, you will

probably invest in an ETF that tracks the NASDAQ 100 index (the ticker symbol for the ETF that

tracks the NASDAQ 100 is QQQ).

6A Short Note on ETF: You can think of an exchange-traded fund as a mutual fund that trades

like a stock. Just like an index fund, an ETF represents a basket of stocks that reect an index such

as the S&P 500. An ETF, however, isnt a mutual fund; it trades just like any other company on

a stock exchange. Unlike a mutual fund that has its net-asset value (NAV) calculated at the end of

each trading day, an ETFs price changes throughout the day, uctuating with supply and demand.

It is important to remember that while ETFs attempt to replicate the return on indexes, there is no

guarantee that they will do so exactly. It is not uncommon to see a 1% or more di¤erence between

the actual indexs year-end return and that of an ETF.

By owning an ETF, you get the diversi cation of an index fund plus the exibility of a stock.

Another advantage is that the expense ratios of most ETFs are lower than that of the average mutual

fund. When buying and selling ETFs, you pay your broker the same commission that youd pay on

any regular trade.

5

maintain a neutral position during Sep and Oct 2017. In the column "Num-

ber of Contracts", calculate the number of put option contracts you need to

maintain in your portfolio on each day in Sep and Oct 2017. What is the theo-

retical return of your hedged portfolio? (Again, please assume a continuously

compounded risk free rate of 3% per year, and a dividend yield of 0. Please use

the implied volatility you obtained in question 2 in your calculation. Assume also

all assumptions of the Black-Scholes model hold.)

V Beta and Delta

1. In CAPM model, reects the covariance of the return of a stock/portfolio with

some benchmark return, for example, the market index. Once we know the of

a portfolio, we can calculate the of the portfolio with respect to the market

index. Here, is de ned as "the increase in the value of the portfolio with

one unit increase in the market index" (An alternative way of interpreting the

concept of in this context is, if NASDAQ 100 increases by $1, by how much

PSCs portfolio is expected to increase?). Here we derive a formula that expresses

of a portfolio (with respect to the market) as a function of its market .

Derivation: Let A0 denote the value of the portfolio at time 0, and AT denote

the value of the portfolio at time T . Then

AT = A0 R

where R is the return on the portfolio. Regressing the portfolio return on that of

the Nasdaq,

R = +RNasdaq + "

where RNasdaq is the return on the market index (in the case, it is the NASDAQ

100 index). Assuming zero dividend yield on the NASDAQ 100 index, we have

RNasdaq =

ST

S0

, where ST denote the NASDAQ 100 index at time T. Therefore we

6

have:

AT = A0

+

ST

S0

+ "

= A0 ( + ") + A0

S0

ST :

The above equation implies that if ST (The NASDAQ 100 index) increase by $1,

then AT (PSCs portfolio) is expected to increase by A0S0 . Therefore PSCs

is:

=

A0

S0

(1)

2. [10 points] Assume PSCs portfolio with respect to NASDAQ 100 is 1:785.

Suppose today is July 26, 2000, PSC decides to short the NASDAQ 100 index to

hedge the market risk. What is the total (dollar) amount of short positions that

PSC should take in the NASDAQ 100 index? (Youll need to check Exhibit 2 in

the case to nd the value of PSCs portfolio on July 26, 2000.)

VI PSCHedging Problem

1. [5 points] What risks does PSC face? How did PSC hedge these risks historically?

Should PSC continue to hedge these risks?

2. [5 points] In Exhibit 3, what is PSCs (with respect to NASDAQ100) in the

"up" days of NASDAQ 100 (Use UP to denote PSCs estimated using data

from "up" days of NASDAQ100)? What is PSCs in "down" days of NASDAQ

100 (Use DOWN to denote PSCs estimated using data from "down" days of

NASDAQ)? Are they equal?

3. [4 points] Suppose PSC decides to short the NASDAQ 100 index to hedge the

market risk. Suppose also it uses UP to calculate and chooses the hedging

strategy. Would this be a good hedge if the market goes up? What if the market

goes down? Is this a perfect hedge?

7

4. [4 points] Answer question 3 assuming PSC now uses DOWN to calculate the

number of short positions

5. [4 points] Answer question 3 assuming PSC uses the average of UP and DOWN

(that is, 1

2

(UP + DOWN)) to calculate the number of short positions.

6. [4 points] If NASDAQ 100 goes up, how would the absolute value of the of a

put option on the index change? What if NASDAQ go down?

7. [4 points] If NASDAQ 100 goes up, how would the absolute value of the of a

call option on the index change? What if NASDAQ go down?

8. [5 points] Instead of shorting the market index to hedge, you can either short call

options to hedge, or long put options to hedge, which is preferable?

9. [5 points] Suppose PSC decided to use options on NASDAQ index to hedge

market risks on July 26, 2000. Among the options listed in Exhibit 10, which

one would you choose? How much positions would you take, why?

8

学霸联盟

Module name: MSIN0107

Module code: Advanced Quantitative Finance

Module leader name: Ming Yang

Academic year: INSERT

Term 1, 2 or 3: INSERT

Type of assessment: Coursework assignment

Nature of assessment – group:

Content of this Assessment Brief

Section Content

A Core information

B Coursework Brief and Requirements

C Module learning outcomes covered in this

assessment

D Assessment criteria

E Groupwork instructions (if applicable)

F Additional information from module leader (if

applicable)

Page 2 of 9

Section A: Core information

This assessment is

marked out of:

100

% weighting of this

assessment within total

module mark

10%

Word count/number of

pages - maximum

1,000 words

There is no penalty for using fewer words pages.

Determining word count

impacted by Turnitin

• After submission to Turnitin, the Turnitin recorded word

count is usually higher than the word count in a Word

document.

• Where the assessment brief specifies a maximum word

count, on the front cover of your submission record the

number of words as recorded in your Word document.

• It is the Word document word count which will be taken

account of in marking, NOT the Turnitin word count.

Footnotes, appendices,

tables, figures, diagrams,

charts included

in/excluded from word

count/page length?

Any footnotes, appendices are not included in page limit.

Bibliographies, reference

lists included

in/excluded from word

count?

Title page, table of contents, any bibliography are excluded from the

page limit.

Penalty for exceeding

specified word

count/page length?

• Where there is a specified word count/page length and this is

exceeded, yes there is a penalty: 10 percentage points

deduction, capped at 40% for Levels 4,5, 6, and 50% for Level

7. Refer to Academic Manual Section 3: Module Assessment -

3.13 Word Counts.

• Where there is no specified word count/page length no

penalty applies.

Requirements for/use of

references

• Where you draw upon sources you must cite them

appropriately.

• As appropriate, you may draw upon a range of sources

including, illustratively, journal articles, other textbooks,

industry reports.

• As appropriate, you may draw upon course materials –

lecture slides, notes, handouts, readings, textbook(s) - you

engaged with in your studying of this module.

• Unless citing content specifically (e.g. a quote from a book)

you should not be copying word for word from lecture slides,

notes, handouts, readings, textbook(s).

• You should capture, articulate and communicate your views,

thoughts and learning in your own words.

• If you do provide quotes from any lecture slides, notes,

handouts, readings, textbook(s) you should cite them and

provide references in the usual way.

Page 3 of 9

• Be aware that a number of academic misconduct checks,

including the use of Turnitin, are available to your module

leader.

• If required/where appropriate UCL Academic Misconduct

penalties may be applied (see immediately below).

Academic misconduct

(including plagiarism)

• Academic integrity is paramount.

• It is expected that your submission and content will be your

own work with no academic misconduct.

• Academic Misconduct is defined as any action or attempted

action, including collusion with other students, that may

result in a student obtaining an unfair academic

advantage. There are severe penalties for Academic

Misconduct, including, where appropriate and required,

exclusion from UCL.

• Refer to Academic Manual Section 9: Student Academic

Misconduct Procedure - 9.2 Definitions.

Submission date 4th March 2021

Submission time 10am UK time

Penalty for late

submission?

Yes. Standard UCL penalties apply. Students should refer to

https://www.ucl.ac.uk/academic-manual/chapters/chapter-4-

assessment-framework-taught-programmes/section-3-module-

assessment#3.12

Submitting your

assignment

The assignment MUST be submitted to the module submission link

located within this module’s Moodle ‘Submissions’ tab by the

specified deadline.

Anonymity of identity.

Normally, all submissions

are anonymous unless

the nature of the

submission is such that

anonymity is not

appropriate, illustratively

as in presentations or

where minutes of group

meetings are required as

part of a group work

submission

Anonymity is required.

Your name should NOT appear anywhere on your submission.

Return and status of

marked assignments

• At the latest this will be within 4 weeks from the date

of submission as per UCL guidelines, but we will

endeavour to return it earlier than this.

• Assessments are subject to appropriate double

marking/scrutiny, and internal quality inspection by

a nominated School of Management internal

assessor. All results when first published are

provisional until confirmed by the relevant External

Examiner and the Examination Board.

Page 4 of 9

• No appeals regarding your published mark are

available until after confirmation by that

Examination Board. UCL regulations specify that

academic judgment applied within the marking

process cannot be challenged.

Uploading your submission

• Unless specifically instructed otherwise in the assessment document, please upload your work as a

single file via the submission link on Moodle.

o Wherever possible you should type/use Excel (as appropriate) for your answers and follow

instructions later in this assessment document.

o If you do have to include any elements that are not typed/computer generated (e.g. figures,

diagrams, equations etc.) as instructed by your module leader, please follow the advice for

submitting handwritten answers for any submission that requires scanning documents. (The

webpage refers to 24-hour timed exams but is applicable to this assessment).

o If you are unable to type your answers for medical reasons, please contact Student Support

and Wellbeing to arrange a SORA and notify your programme administrator.

o If for any reason you are not able to use the app recommended by ISD at the link above, you

can consult the following resources for advice about preparing your submission:

Submitting handwritten assignments to Moodle using mobile or tablet Devices -

Device Camera

Submitting handwritten assignments to Moodle using mobile or tablet devices - MS

One Drive App

• Please DOUBLE CHECK that the file you are uploading is the correct one and is complete (with all

pages visible). You should only submit your final version of the work to the submission box. Once the

original deadline has passed, any submission made to the official submission box will be taken as

the final submission. Work submitted after the original submission deadline will NOT be removed

and a new version cannot be submitted. If you wish to check your work before submitting your final

version, you can use the Turnitin Drafts Checker rather than your official submission inbox. Please be

sure that the version of the assignment you submit is the version you intend to be marked for that

module. If you are granted ECs in relation to a piece of work already submitted, the mitigation

applied will be a deferral and not an extension. If you are unable to submit on time, you may submit

an EC form to request an extension if you have legitimate mitigating circumstances.

Page 5 of 9

Technical Problems

If you encounter difficulties submitting your assessment via Moodle, then please immediately notify (by

email) your department (Programme Administrators ONLY), explaining the problem and including a copy of

the work you are trying to submit. ONLY use this approach if you can show that you have tried to download

from/upload to Moodle and encountered technical difficulties.

Advice and other support

• Student Support and Wellbeing

Page 6 of 9

Section B: Coursework Brief and Requirements

See document at the end of the brief.

Page 7 of 9

Section C: Module Learning Outcomes covered in this

Assessment

This assignment contributes towards the achievement of the module Learning

Outcomes as specified in the module description.

Page 8 of 9

Section D: Assessment criteria

Within each section of this coursework you may be assessed on the following aspects, as

applicable and appropriate to this particular assessment, and should thus consider these aspects

when fulfilling the requirements of each section:

• The accuracy of any calculations;

• The strengths and quality of your overall analysis and evaluation;

• Appropriate use of relevant theoretical models, concepts and frameworks;

• The rationale and evidence that you provide in support of your arguments;

• The credibility and viability of the evidenced conclusions/recommendations/plans of

action you put forward;

• Structure and coherence of your considerations and reports;

• As and where required, relevant and appropriate, any references should use either

the Harvard OR Vancouver referencing system (see References, Citations and

Avoiding Plagiarism)

• Academic judgement regarding the blend of scope, thrust and communication of

ideas, contentions, evidence, knowledge, arguments, conclusions.

• Each part has requirements with allocated marks, maximum word count limits/page

limits and where applicable, templates that are required to be used.

You are advised to refer to the UCL Assessment Criteria Guidelines, located at

https://www.ucl.ac.uk/teaching-learning/sites/teaching-learning/files/migrated-

files/UCL_Assessment_Criteria_Guide.pdf

Page 9 of 9

Section E: Groupwork Instructions

This is a team assignment. Each team should submit a pdf version report in Moodle. The

report should contain your answers/arguments and will be graded. Please also prepare

Powerpoint slides that summarize your findings. You don't have to submit the Powerpoint

slides in Moodle. In class, I may randomly select one or two teams to present their

Powerpoint slides.

This assignment is due at 10am on 4th March, 2021. See the assignment instructions here

and data here.

You'll need to use the Black-Scholes formula to calculate option prices and implied volatility.

To make your life easy, here I provide two useful Excel add-ins: optall3.xla and

optbasic3.xla. Please put the add-ins to "C:\Program Files\Microsoft Office\Office16\Library"

and then install the two add-ins. To install the add-ins, open any Excel spreadsheet --> file -

-> options --> add-ins --> choose "Excel add-ins" in the bottom box and click "go" -->

browse and choose the two add-ins at the path where you put them --> click "ok".

These add-ins are provided in a CD published with the "McDonald" textbook (Derivatives

Markets, Third Edition, Robert L. McDonald, Addison Wesley, Copyright 2013) and are thus

intended for educational, non-commercial use. Neither the author nor publisher represent

these spreadsheets as suitable for any purpose other than to help you learn the material in

the text.

Section F: Additional information from module leader(s)

N/A

MSIN0107: Advanced Quantitative Finance

UCL School of Management

Prof. Yang

m-yang@ucl.ac.uk

Group Course Work 2

I Introduction and Instructions

Please read the HBS case 9-201-071 Pine Street Capital carefully, and answer the

following questions.

A Black-Scholes Functions

Youll need to use the Black-Scholes formula to calculate option prices and implied

volatility. To make your life easy, here I provide two useful Excel add-ins:1 op-

tall3.xla and optbasic3.xla. Please put the add-ins to "C:nProgram FilesnMicrosoft

O¢ cenO¢ ce16nLibrary" or "C:nProgram Files (x86)nMicrosoft O¢ cenrootnO¢ ce16nLibrary"

and then install the two add-ins. To install the add-ins, open any Excel spreadsheet

> le > options > add-ins > choose "Excel add-ins" in the bottom box and click

"go" > browse and choose the two add-ins at the path where you put them > click

"ok".

Once the add-ins are installed, you should be able to use the Excel functions in the

table below. (You may just need to use a few of them, e.g., BSCallImpVol, BSPut,

BSPutDelta, etc. You may want to play with others so I include all the functions here

FYI.) The following symbol de nitions are used in these functions: s= stock price,

k= strike price, v= volatility (annualized), r= interest rate (continuously-

compounded, annualized), t= time to expiration (years), and d= dividend yield

(continuously-compounded, annualized).

1These add-ins are provided in a CD published with the "McDonald" textbook (Derivatives Mar-

kets, Third Edition, Robert L. McDonald, Addison Wesley, Copyright 2013) and are thus intended

for educational, non-commercial use. Neither the author nor publisher represent these spreadsheets

as suitable for any purpose other than to help you learn the material in the text.

1

Function De nition Function Description

BSCall(s, k, v, r, t, d) European call option price

BSPut(s, k, v, r, t, d) European put option price

BSCallDelta(s, k, v, r, t, d) European call delta

BSPutDelta(s, k, v, r, t, d) European put delta

BSCallGamma(s, k, v, r, t, d) European call gamma

BSPutGamma(s, k, v, r, t, d) European put gamma

BSCallVega(s, k, v, r, t, d) European call vega

BSPutVega(s, k, v, r, t, d) European put vega

BSCallRho(s, k, v, r, t, d) European call rho

BSPutRho(s, k, v, r, t, d) European put rho

BSCallTheta(s, k, v, r, t, d) European call theta

BSPutTheta(s, k, v, r, t, d) European put theta

BSCallPsi(s, k, v, r, t, d) European call psi

BSPutPsi(s, k, v, r, t, d) European put psi

BSCallElast(s, k, v, r, t, d) European call elasticity

BSPutElast(s, k, v, r, t, d) European put elasticity

BSCallImpVol(s, k, v, r, t, d, c) Implied volatility for European call2

BSPutImpVol(s, k, v, r, t, d, c) Implied volatility for European put3

BSCallImpS(s, k, v, r, t, d, c) Implied stock price for a given European call option price

BSPutImpS(s, k, v, r, t, d, c) Implied stock price for a given European put option price

II Case Summary

Pine Street Capital (PSC) is a technology hedge fund located in San Francisco, Cali-

fornia. PSC manages a fund that invests primarily in semiconductor companies that

produce integrated circuits for broadband communications including wide and local

area networks, optical components, and storage area networks. It is currently July,

2000 in the case, and the NASDAQ market (where most of the stocks that PSC invests

in are traded) index reached a peak of over 5,000 a few months ago but has dropped

2The option price is entered as c; the volatility entered does not matter.

3The option price is entered as c; the volatility entered does not matter.

2

considerably since then. In addition, the NASDAQ has experienced a historically un-

precedented amount of volatility over the last several months, as shown in Exhibit 7

of the case. Due to the market drop and volatility, PSCs fund has experienced con-

siderable problems in the last few months. Even though the fund has had a policy

of hedging market risk, the fund has nevertheless experienced large losses on many

days (sometimes on several consecutive days) in the last few months. This has created

problems for the fund because of the leverage employed by the fund. Some of the

losses that the fund had experienced had been large enough that the fund had come

dangerously close to having its prime broker, a prominent Wall Street rm, liquidate

the fund. Harold Yoon, a partner in the fund, now must evaluate the funds market

hedging program over the last few months to determine why the fund had experienced

such large losses on many days.

III Derivatives and Leverage

Consider the following binomial tree of the price movement of a non-dividend-paying

stock, assume the time period is one year (i.e., h = 1), and the e¤ective one-year

interest rate is 20% (i.e., er1 = 1 + 20%).

% Su = 140

S0 = 100

& Sd = 90

1. [2 points] Please calculate u and d, the gross returns on the stock for both states

of the world.

2. [5 points] Consider an at-the-money European call option with maturity of 1

year. Compute the and B of the call option. What is the gross return on a

long position in the call option (You need calculate the return on the call option

at both nodes, u and d)?

3. [3 points] Is the call option riskier than the stock? Why? Sometimes we say a

call option is like a leveraged position on the underlying stock, comment on this.

3

4. [3 points] Consider a futures contract on one share of the stock. What is the

no-arbitrage futures price (i.e., the forward price), F0;T?

5. [5 points] Assume an initial margin requirement of 8:33% of the futures price,

F0;T . What is the return on a long position in the futures contract? (Again, the

realized return will depend on the state of the world. Also, note that balances on

the margin account will earn risk-free return.) What is the expected return on

the futures contract under the risk-neutral probability? Is the futures contract

riskier than the stock?

6. [7 points] Can you invest in stocks and a risk-free bond to replicate the payo¤

of the futures contact, how? (You need to take into account that investing in

the futures contract involves an initial investment in the margins account.) Is

the futures contract in the above example a leveraged position in the underlying

stock?

IV Hedging with Put Options

1. [5 points] Use the historical data on NASDAQ 100 index in the Excel le NAS-

DAQ Index_PSC.xlsx 4 to estimate the volatility of the NASDAQ 100 index

during the sample period.

Hint: You need to rst get the data series for ln

St+1

St

, and estimate the stan-

dard deviation of the log return process (Recall that we assume the log return

process is i.i.d. normal). Since you are using monthly data, you need to trans-

form the monthly estimate into annual volatility. You can do so by using the

following formula:

Annual = Monthly

p

12

2. [5 points] Suppose on Sep 30, 2018, an at-the-money European call option on

the NASDAQ 100 index with maturity of 1 year is traded at $425.7661. Assume

the continuously compounded LIBOR is 3% per annum, and the continuously

4This can be downloaded from the course website.

4

compounded dividend yield is 0%. What is the implied volatility of the NASDAQ

100 index (from the Black-Scholes model)?

3. [5 points] Please nd the data for the NASDAQ 100 index during Sep and

Oct 2017 in the spread sheet named "Oct 2017" in the Excel le NASDAQ In-

dex_PSC.xlsx. Consider an at-the-money European put option on one NASDAQ

100 index on Sep 21, 2017. The maturity of the option is one year (the option

expires on Sep 21, 2018, i.e. the third Friday of September, 2018. Take 1 year as

252 trading days, and each trading day as 1/252 year). Calculate the theoretical

Black-Scholes prices of this put option for each day in the spreadsheet Oct 2017

and ll in the column "BS Put Price". Please use the continuously compounded

annual interest of 3% per year. Please use the implied volatility you obtained in

part 2 when calculating the Black-Scholes prices.

4. [5 points] Suppose you invested 1 million US dollar in the NASDAQ 100 index 5 6

on Sep 21, 2017. Suppose you want to use the above put option on NASDAQ 100

index (That is, the at-the-money put option on the index with one year maturity

described in the last question) to hedge the risks of your investment. To construct

a neutral position, how many put option contracts do you need to purchase

on Sep 21, 2017? (Note that each put option contract on the index contains 100

put options on the index. Assume you can take fractions of an option contract.)

5. [5 points] Suppose you rebalance your position in the put option everyday to

5Of course, trading the NASDAQ 100 index directly can be very costly. In practice, you will

probably invest in an ETF that tracks the NASDAQ 100 index (the ticker symbol for the ETF that

tracks the NASDAQ 100 is QQQ).

6A Short Note on ETF: You can think of an exchange-traded fund as a mutual fund that trades

like a stock. Just like an index fund, an ETF represents a basket of stocks that reect an index such

as the S&P 500. An ETF, however, isnt a mutual fund; it trades just like any other company on

a stock exchange. Unlike a mutual fund that has its net-asset value (NAV) calculated at the end of

each trading day, an ETFs price changes throughout the day, uctuating with supply and demand.

It is important to remember that while ETFs attempt to replicate the return on indexes, there is no

guarantee that they will do so exactly. It is not uncommon to see a 1% or more di¤erence between

the actual indexs year-end return and that of an ETF.

By owning an ETF, you get the diversi cation of an index fund plus the exibility of a stock.

Another advantage is that the expense ratios of most ETFs are lower than that of the average mutual

fund. When buying and selling ETFs, you pay your broker the same commission that youd pay on

any regular trade.

5

maintain a neutral position during Sep and Oct 2017. In the column "Num-

ber of Contracts", calculate the number of put option contracts you need to

maintain in your portfolio on each day in Sep and Oct 2017. What is the theo-

retical return of your hedged portfolio? (Again, please assume a continuously

compounded risk free rate of 3% per year, and a dividend yield of 0. Please use

the implied volatility you obtained in question 2 in your calculation. Assume also

all assumptions of the Black-Scholes model hold.)

V Beta and Delta

1. In CAPM model, reects the covariance of the return of a stock/portfolio with

some benchmark return, for example, the market index. Once we know the of

a portfolio, we can calculate the of the portfolio with respect to the market

index. Here, is de ned as "the increase in the value of the portfolio with

one unit increase in the market index" (An alternative way of interpreting the

concept of in this context is, if NASDAQ 100 increases by $1, by how much

PSCs portfolio is expected to increase?). Here we derive a formula that expresses

of a portfolio (with respect to the market) as a function of its market .

Derivation: Let A0 denote the value of the portfolio at time 0, and AT denote

the value of the portfolio at time T . Then

AT = A0 R

where R is the return on the portfolio. Regressing the portfolio return on that of

the Nasdaq,

R = +RNasdaq + "

where RNasdaq is the return on the market index (in the case, it is the NASDAQ

100 index). Assuming zero dividend yield on the NASDAQ 100 index, we have

RNasdaq =

ST

S0

, where ST denote the NASDAQ 100 index at time T. Therefore we

6

have:

AT = A0

+

ST

S0

+ "

= A0 ( + ") + A0

S0

ST :

The above equation implies that if ST (The NASDAQ 100 index) increase by $1,

then AT (PSCs portfolio) is expected to increase by A0S0 . Therefore PSCs

is:

=

A0

S0

(1)

2. [10 points] Assume PSCs portfolio with respect to NASDAQ 100 is 1:785.

Suppose today is July 26, 2000, PSC decides to short the NASDAQ 100 index to

hedge the market risk. What is the total (dollar) amount of short positions that

PSC should take in the NASDAQ 100 index? (Youll need to check Exhibit 2 in

the case to nd the value of PSCs portfolio on July 26, 2000.)

VI PSCHedging Problem

1. [5 points] What risks does PSC face? How did PSC hedge these risks historically?

Should PSC continue to hedge these risks?

2. [5 points] In Exhibit 3, what is PSCs (with respect to NASDAQ100) in the

"up" days of NASDAQ 100 (Use UP to denote PSCs estimated using data

from "up" days of NASDAQ100)? What is PSCs in "down" days of NASDAQ

100 (Use DOWN to denote PSCs estimated using data from "down" days of

NASDAQ)? Are they equal?

3. [4 points] Suppose PSC decides to short the NASDAQ 100 index to hedge the

market risk. Suppose also it uses UP to calculate and chooses the hedging

strategy. Would this be a good hedge if the market goes up? What if the market

goes down? Is this a perfect hedge?

7

4. [4 points] Answer question 3 assuming PSC now uses DOWN to calculate the

number of short positions

5. [4 points] Answer question 3 assuming PSC uses the average of UP and DOWN

(that is, 1

2

(UP + DOWN)) to calculate the number of short positions.

6. [4 points] If NASDAQ 100 goes up, how would the absolute value of the of a

put option on the index change? What if NASDAQ go down?

7. [4 points] If NASDAQ 100 goes up, how would the absolute value of the of a

call option on the index change? What if NASDAQ go down?

8. [5 points] Instead of shorting the market index to hedge, you can either short call

options to hedge, or long put options to hedge, which is preferable?

9. [5 points] Suppose PSC decided to use options on NASDAQ index to hedge

market risks on July 26, 2000. Among the options listed in Exhibit 10, which

one would you choose? How much positions would you take, why?

8

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