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excel代写-MSIN0104
时间：2021-11-08
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 self-
contained, but you must submit an accompanying excel spreadsheet with your
computations.
Section A Question 1 Word count: Max 150 words + spreadsheet
1 At the end of each year, interest is due on the balance outstanding at the beginning of the year.
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 risk-
aversion 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:
o 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.
o 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] = 32.
[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
学霸联盟
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 self-
contained, but you must submit an accompanying excel spreadsheet with your
computations.
Section A Question 1 Word count: Max 150 words + spreadsheet
1 At the end of each year, interest is due on the balance outstanding at the beginning of the year.
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 risk-
aversion 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:
o 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.
o 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] = 32.
[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
学霸联盟
