Assessment Information for Online Exam  Module name: MSIN0104 Module code: Introduction to Quantitative Finance Module leaders names: Frederic Malherbe and Wei Cui Academic year: 2020-21 Term 1, 2 or 3: 1 Type of assessment: Online Exam Nature of assessment – individual or group: Individual   Content of this Assessment Brief Section Content A Core information B 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)   Section A: Core information This assessment is marked out of: 100 ma rks % weighting of this assessment within total module mark 60%   Time allowed for     completion of this assessment ?   This assessment should take approximately 2 hours to complete

Assessment Information for Online Exam 

Module name: MSIN0104

Module code: Introduction to Quantitative Finance

Module leaders names: Frederic Malherbe and Wei Cui

Academic year: 2020-21

Term 1, 2 or 3: 1

Type of assessment: Online Exam

Nature of assessment – individual or group: Individual

Content of this Assessment Brief

Section A: Core information

Academic Support with this Assessment  

Given the nature of this assessment, during the exam window no questions should be directed to the Module Leader/Module Team. If you have doubts about wording or requirements etc., state your assumptions. If they are appropriate they will be taken into consideration in marking.

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.
  • Wherever possible you should type/use Excel for (as appropriate) your answers and follow instructions later in this assessment document.
  • If you do have to include any elements that are not typed/computer generated (e.g.

figures, diagrams, equations etc.), or you are unable to type your answers for any reason, 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 all online submissions including this one).

• • 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). Resubmission will not be permitted.

Technical Problems

If you encounter difficulties downloading or 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

Section B: Assessment Requirements

See exam paper attached at the end of the brief.

 Section C: Module Learning Outcomes covered in this Assessment

This assignment contributes towards the achievement of the following stated module Learning Outcomes as below:

1. Being able to use mathematic tools such as derivatives, limits, optimisation, probability theory, stochastic calculus, and linear algebra to formalize quantitative problems in finance. 
2. Being able to solve such problems. 
3. A deep understanding of the foundational concepts of quantitative finance, such as time value of money, interests compounding, portfolio choice, and the fundamentals of the pricing of bonds, stocks, call and put options, and other derivatives.

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/migratedfiles/UCL_Assessment_Criteria_Guide.pdf   

Section E: Groupwork Instructions 

• Not applicable as this is an individual assessment

Section F: Additional information from module leaders

You should save your work using the module code and your candidate number as the file name (e.g. “MSIN0104_ABCD1” where you should replace “ABCD1” with your candidate number).  

Your submission should include two parts: 

·        The exam paper   

·        The accompanying Excel file which should contain three sheets, each named: Q1, Q2, and Q9 respectively.  

The name of these two documents MUST RESPECT the following format: module number_candidate number:  

·        Exam paper: “MSIN0104_ABCD1.pdf”  

·        Excel file : “MSIN0104_ABCD1.xlsx”  

You should have already received an email with your candidate number. If you do not know your candidate number, please contact Magali Sainte-Luce at mgmt.finance-admin@ucl.ac.uk. 

MSIN0104

Introduction to Quantitative Finance Online Examination Paper

2020/21

Examination length: TWENTY-FOUR (24) hours

There are THREE (3) sections to the examination paper.

Section A consists of TWO (2) questions on Part I of the module. This section is worth FOURTY (40) marks.

Section B consists of SIX (6) true/false/uncertain questions. This section is worth THIRTY (30) marks.

Section C consists of ONE (1) question on Part II of the module. This section is worth THIRTY (30) marks.

You are advised to allocate your time between the three sections in proportion to the marks available.

Module Leader/Internal Examiner: Profs Frederic Malherbe / Wei Cui

TURN OVER

SECTION A [40 marks]

Question 1: Time value of money and loan valuation [20 marks]

Ross wants to buy a new mansion. He needs a £10m mortgage (for simplicity we ignore the currency unit from now on). He tells Barkley’s Bank that he wishes to borrow over a 20-year horizon. The bank offers him two alternatives:

Alternative A: A fixed rate of 3% for the whole duration.

Alternative B: A floating rate of LIBOR + 1.5%, with two 10-year periods of fixed rates.

• Currently, the LIBOR is at 1%, so the rate will be fixed at 2.5% for the first 10 years. 
• Then, a new, fixed interest rate will apply from year 11 to 20. It will be set according to the LIBOR on the last day of year 10.

Assume that Ross is risk-neutral and believes that, in 10 years, LIBOR will either be 1.5% or 4%, with equal probabilities

To simplify, assume that the mortgage is an amortising loan with annual payments.^[1]

1. Compute the annual repayment under alternative A.
2. Compute the balance at the end of year 10 under alternative B and the repayment after the new rate has been set (consider both possible rates). 
3. Discuss under which conditions Alternative A is better for Ross than Alternative B. 

Please report your answers and explain carefully how you obtained them. Please make sure to clearly state any assumption you felt necessary to make. Your report should be selfcontained, but you must submit an accompanying excel spreadsheet with your computations. 

Section A Question 1 Word count: Max 150 words + spreadsheet

Question 2: Portfolio selection [20 marks]

Consider an environment with two risky assets and a risk-free bond. You start with £1 million. Using the risk-free bond, you can save at the risk-free rate, but you cannot borrow. 

Instructions

• Please use the data from the spreadsheet MSIN104_EXAM20_DATA.
• Follow the instruction to generate personalised parameters for you. To make sure you don’t make a mistake, there’s an illustration at the end of this question. The number you will enter in Cell A2 is called “Your data generating number”.  Once you will have entered your data generating number in Cell A2, the spreadsheet will display all the needed parameters and the distribution of returns of the risky assets (you are looking at only one period ahead, in which there are 20 possible states).

1. Compute and report the Sharpe Ratio of both risky assets
2. Find the portfolio (i.e. the combination of the three assets) that maximises the following mean-variance utility

?(?, ?) = ? − ??²

           where   is the expected return on the portfolio,  ?²  its variance, and  the riskaversion parameter you will find in cell B5.

Please report your data generating number and your answers (the Sharpe Ratios, the weights, and the maximal utility) and explain carefully how you obtained them. Your report should be self-contained. Please make sure to clearly state any assumption you felt necessary to make. 

Appendix: Illustration on how / where to enter your data generating number.

• When you open the worksheet, you will see

• Except that you will see another number than 6831 (unless there’s a huge coincidence). Type the number you see into Cell A2 and save the spreadsheet. This will generate the parameters you need. For example, here is what happened when I entered 6831 in Cell A2:

• Remarks:
  • Now, the number in Cell A1 has changed. This is normal as Excel generates new random numbers every time it performs any calculation (including just

“storing” a number you have entered). From now on, just ignore Cell A1.

• • The parameters (risk-free rate and risk aversion) are determined by the value in Cell A2. Do not modify the value of this cell as this would change the parameters and affect the answers to the questions. o You MUST report your data generating number in your exam script. If you fail to do so, or make a mistake while reporting it, you will get zero mark for this question.   

Section A Question 2 Word count: Max 200 words + spreadsheet

SECTION B [30 Marks]

IMPORTANT:

Answer all questions. 

For each question, identify the statement as True/False/Uncertain. You must explain your reason for answering True/False/Uncertain. You may use verbal, diagrammatic and mathematical arguments as appropriate. 

Questions 3 to 8 [5 marks each]

3. Money printing is the main driver of inflation in the short term (up to 1 year).

4. Assume that, for some time, inflation had been stable at 3%, while the Central Bank target nominal rate was 5%. Now, inflation has suddenly increased to 3.5%. To cool down the economy, the Central Bank must increase its target nominal rate to 5.5%.

5. An investor is expecting the stock price of a big-tech company to go up. Speculating by using forwards/futures is less expensive to buy than using call options (with the same strike price and time-to-maturity).

6. The early exercise of an American put option becomes more attractive as the risk-free rate falls and the volatility of the underlying asset price increases. 

7. [The context] A symmetric butterfly spread has positions in options with 3 different strike prices. It can be created by buying a call option with a relative low strike price ?₁, buying a call option with a relatively high strike price ?₃, and selling two call options with a strike price ?₂ = 0.5(?₁ + ?₂). It can also be created by using put options. 

[The statement] The cost of a butterfly spread created from European puts is smaller than the cost of a butterfly spread created from European calls (with the same strike prices and expiration dates).

8. If ?_? follows a Brownian motion, then ?[?_?⁴] = 3?². 

[Hint] You can use Ito’s Lemma: ??(?_?) = (?_?(?_?)?(?_?, ?) + 0.5?_??(?_?)?²(?_?, ?))?? + ?_?(?_?)?(?_?, ?)??_?, where {?_?, ? ≥ 0} is an Ito process with ?(?_?, ?) as the drift and ?(?_?, ?) as the volatility.

Section B Word count: Max 100 words per question

CONTINUED

SECTION C [30 marks]

Question 9: Options [30 marks]

The price of a stock is currently 100 USD. Assume the price can increase by a factor of

1.10 or fall by a factor of 0.90. The stock pays no dividends and the annual percentage rate (APR) is 2%. Consider an American put option on this stock with a strike price of 95 USD, and with two years to maturity and one-year step length. You are standing at year ? = 0 currently.

1. What is the price of this American put option at year ? = 0? 

2. Suppose the strike price is 95 + ?, where  is the day of the month when you were born. What is the price of this American put option at year ? = 0?

3. What if the interest rate is doubled? Compare your result with (1). Then, using (2) and

(3), explain how strike price and interest rate affect the put option price.

Section C Question 9 Word count: Max 350 words + spreadsheet or tables

END OF PAPER