PAPER CODE NO.
MATH 377
EXAMINER: O. Menoukeu Pamen TEL.NO. 44393
DEPARTMENT: Mathematical Sciences
MARCH 2021 MOCK PAPER
Financial and Actuarial Modelling in R
Time allowed: 90 minutes
INSTRUCTIONS TO CANDIDATES:
All answers will be taken into account. The marks noted indicate
the relative weight of the questions out of 50 marks in total.
By submitting solutions to this assessment you affirm that you
have read and understood the Academic Integrity Policy detailed in
Appendix L of the Code of Practice on Assessment.
Note that this mock paper is designed to show you the style of the
midterm exam.
Paper Code MATH 377 Page 1 of 3 CONTINUED
1. (a) Write a R program to create three vectors x, y, z with 4 integers. Com-
bine the three vectors to become a 4 × 3 matrix where each column
represents a vector. Print the content of the matrix. [4 marks]
(b) Write a R program to:
(i) create two vectors of v1 = 6 and v2 = 14 random numbers that are
uniformly distributed between -5 and +5. [4 marks]
(ii) create an array of three 3 × 6 matrices each with 3 rows and 6
columns from the above given two vectors. [3 marks]
(iii) print the second column of the first matrix of the array.
[2 marks]
(iv) print the columns of third matrix such that the element in the last
line is bigger than the mean of v1. [3 marks]
2. A manager has a portfolio of three stocks A, B and C and one risk free asset
(Bond) that yields a rate of 2%. The probability distribution of the risky
portfolio is as follows:
Stock A Stock B Stock C
Expected return 11% 14% 8.5%
Standard deviation 30% 45% 30%
Table 1: Probability distribution of the stocks
The correlation between the stock returns are: ρAB = 0.3, ρAC = 0.15 and
ρBC = 0.45.
(a) Write a R program to find the mean and variance of an equally weighted
portfolio. [3 marks]
(b) Write a R program to plot the portfolio opportunity. [5 marks]
(c) Write a R program to find the Sharpe ration and plot the capital market
line. [3 marks]
(d) Write a R program to find a minimum variance portfolio with the return
12%. Find the weight of each stocks in this portfolio. [5 marks]
3. A stock price is currently £30. Over each of the next two 4-month periods
it is expected to increase by 15% or decrease by 20%. The risk-free interest
rate is 5% per annum with continuous compounding during the first 4-month
period and 6% per annum with weekly compounding during the second 4-
month period.
Write a R program to find the initial value of a 8-month American style
option that pays off V (T ) = max(2{6−√S(T )}, 0), where S(T ) is the stock
price in eight months. [6 marks]
Paper Code MATH 377 Page 2 of 3 CONTINUED
4. A stock price is currently £50. It is known that at the end of 3 months it will
increase by 8% or decrease by 12%. The risk-free interest rate with monthly
compounding is 10% per annum.
(a) Write a R program to find the initial value of a 3-month European call
option on the stock with an exercise price of £48. [5 marks]
(b) Describe the hedging strategy for the seller of the option. [3 marks]
(c) Assume that the initial value of the 3-month option is £4. Explain how
to make a risk free profit. [4 marks]
Paper Code MATH 377 Page 3 of 3 END