Tasks to be solved in CW I:  Basic Application with MATLAB

The following questions are designed to examine whether you have learned the basics of MATLAB. Please note Question 1 to 3 are must-taken ones because demos and    substantial hints are demoed in the on-site sessions (also available in the recording).

1.     What is the value of lim Sn

where Sn  = ∑1  ?

What is the min n such that Sn  approaches its limit with tolerance < 10 −5? Write a function, “Sn_calculator” to calculate Sn  and demonstrate this in a script.

2.     Examine the log return of APPL data in ‘Volatility_Estimation - APPL a- weighted’ (B2:B521).

✓  Plot the histogram of the log return.

✓  Compare the above with the fitted normal distribution.

✓  Visualize the comparison in a figure.

✓  Implement everything in a script, i.e., you need to find a way to import the data into MATLAB.

3.     Try to write a code, ‘Newton_0’ , which implements Newton’s method with the initial guess, x0 , f and df (derivative of f) as the input. Find the implied volatility of Example 2 in the MATLAB Notes 4 with the “Newton_0” .

4.     Consider the following investment:

A start-up company just got 70 million from the angel investor. Based on its business plan, it is expected to generate 25 million after-tax profits in the end of each year for 5 years with this financing. What is the IRR recognized by the angel investor? Use the ‘Newton_0’ developed in 1.

5.     For any positive integer n, define the function f as follows:

f(n) = { 2

if n ≡ 0 (mod 2)

if n ≡ 1 (mod 2)

The Collatz conjecture tells us if we form a sequence by performing f iteratively, the resulting sequence, (a0, … ai )

ai  = {f(ai−1)

for i = 0

fori > 0

will reach 1 and end up with 4, 2, 1, … . repeatedly.

The total stopping time of n is defined as the smallest k such that ak  = 1.

Among integers, 1,… .,200, find which has the largest total stopping time, kmax and what the corresponding kmax  is.

6.     Practical problem solving

Suppose we are in the FIN303 economy where there are currently 2 financial assets   traded, including the risk-free bond with 5-year time to maturity, the stock ofAIHSM Inc. The public information about these assets is summarized in the table below:

a.     Based on the public information, what should be the continuous risk-free interest rate reflected in the economy? Find your answer with the Newton’s method and double-check it with a different method.

b.     Based on the historical data of AIHSM Inc., calculate the volatility of the stock return with EWMA scheme. Provide a prediction of the volatility tomorrow. For simplicity, calculate the VL  as the overall variance of the data.

c.     Suppose you have a $10M position on the stock ofAIHSM Inc. Apply the historical simulation method with volatility updating scheme (apply the estimate in b.) to estimate the corresponding 1-day VaR and ES and assess whether your position is risky.

d.     Try to estimate the ‘probability’ that the stock price of AIHSM Inc. will exceed $200. Elaborate on your idea and provide the estimated probability.

Please note that you can essentially apply any techniques to solve the questions, but everything needs to be done with MATLAB. In addition, all questions count.

Marking Criteria and Guidelines:

➢  Report2 :

There is no need to write a formal report for this mini project. Instead, your group only needs to illustrate how the questions are solved and demonstrate the results   in the report. You don’t have to review standard techniques or materials covered   in this module.

Note that it is better to use proper tables and/or figures to show the results. A critical summary or a step-by-step outline would be enough to show your ideas.

➢  Code:

Code will be part of the assessment to examine your learning outcomes. Please try to design your codes as best as you can. For example, efficient and well-structured codes with critical comments may be strengths in the context of programming. By contrast, messy lines, and redundant loops with no comments in the codes may reflect worse programming capability or habits.

On top of all, being runnable and generating consistent results in the report are the most important things your group should follow.

Final reflection:

Reflect the limitations or thoughts you have. If feasible, try to come up with ideas or  potential ways to improve the current achievement or analysis. Ideas will be fine even if you don’t know how to program them yet.

Please do not copy and paste your codes in the report. Besides, it is not necessary to explain how the code is designed in the text.