# Stochastic FinanceStochastic Finance

Stochastic Finance

Stochastic Finance
M081LON
[NEW ] Mid-Term Assignment
Issued: Week 1 of the current term
This is an INDIVIDUAL Summative Assignment.
Section 1.0
The Requirements
Question 1 (20 Marks)
A stockâ€™s terminal value S has a uniform distribution: that is, it is equally likely to
assume any value in the range (0-100) and will not assume any value outside of this
range. The random variable x on which this stockâ€™s value is based has a density
function p(x) =1 for 0 = x = 1 and 0 elsewhere. The stockâ€™s random terminal value is
f(x) =100x.
(a)
Find the distribution function P(x) for p(x)
(2 marks)
(b)
Find the expected value of the stockâ€™s terminal S value assuming it will fall within
the range (i) 50-100; (ii) 0 â€“ 50; (iii) 0 to 100.
(6 marks)
(c)
Find the variance of S in the range 0 â€“ 100 (6 marks)
(d)
What would be the expected future cash flow (contingent on its exercise) of a call
option written on this stock if its exercise price were \$50? That is, what is the
expected cash flow of the option conditional on its exercise?
(6 marks)
Question 2 (30 Marks)
Burton Gordon Malkiel (a fierce supporter of Efficient Market Hypothesis), in his
book â€œA Random Walk Down Wall Streetâ€, claims that the daily logarithmic changes
in the closing price of stock follow a random walkâ€”that is, these daily events are
independent of each other and move upward or downward in a random mannerâ€”and
can be approximated by a normal distribution. To test this theory, use either a printed
or electronic financial mediums (i.e. including Bloomberg) to identify/select one
company traded on the NYSE, one company traded on the American Stock Exchange
and one company traded on the NASDAQ, and then carry out the following tasks:
(a)
Use Yahoo Finance or the Bloomberg terminal to obtain the daily closing stock price
of each of these companies of the past six consecutive weeks (so that you have 30
values per company). (5 marks)
(b)
Compute the logarithmic daily changes in the closing stock price of each of these
companies for six consecutive weeks (so that you have 30 values per company) using
the formula:

Where St is the share price in period t and St-1 is the share price in the previous period.
(5 marks)
(c)
For each of your six data sets, decide whether the data are approximately normally
distributed by a normal probability plot, a box and whisker graph, and the descriptive
statistics summary. Compare data characteristics to theoretical properties.
(5 marks)

# Our Service Charter

1. ### Excellent Quality / 100% Plagiarism-Free

We employ a number of measures to ensure top quality essays. The papers go through a system of quality control prior to delivery. We run plagiarism checks on each paper to ensure that they will be 100% plagiarism-free. So, only clean copies hit customers’ emails. We also never resell the papers completed by our writers. So, once it is checked using a plagiarism checker, the paper will be unique. Speaking of the academic writing standards, we will stick to the assignment brief given by the customer and assign the perfect writer. By saying “the perfect writer” we mean the one having an academic degree in the customer’s study field and positive feedback from other customers.
2. ### Free Revisions

We keep the quality bar of all papers high. But in case you need some extra brilliance to the paper, here’s what to do. First of all, you can choose a top writer. It means that we will assign an expert with a degree in your subject. And secondly, you can rely on our editing services. Our editors will revise your papers, checking whether or not they comply with high standards of academic writing. In addition, editing entails adjusting content if it’s off the topic, adding more sources, refining the language style, and making sure the referencing style is followed.
3. ### Confidentiality / 100% No Disclosure

We make sure that clients’ personal data remains confidential and is not exploited for any purposes beyond those related to our services. We only ask you to provide us with the information that is required to produce the paper according to your writing needs. Please note that the payment info is protected as well. Feel free to refer to the support team for more information about our payment methods. The fact that you used our service is kept secret due to the advanced security standards. So, you can be sure that no one will find out that you got a paper from our writing service.
4. ### Money Back Guarantee

If the writer doesn’t address all the questions on your assignment brief or the delivered paper appears to be off the topic, you can ask for a refund. Or, if it is applicable, you can opt in for free revision within 14-30 days, depending on your paper’s length. The revision or refund request should be sent within 14 days after delivery. The customer gets 100% money-back in case they haven't downloaded the paper. All approved refunds will be returned to the customer’s credit card or Bonus Balance in a form of store credit. Take a note that we will send an extra compensation if the customers goes with a store credit.

We have a support team working 24/7 ready to give your issue concerning the order their immediate attention. If you have any questions about the ordering process, communication with the writer, payment options, feel free to join live chat. Be sure to get a fast response. They can also give you the exact price quote, taking into account the timing, desired academic level of the paper, and the number of pages.

Excellent Quality
Zero Plagiarism
Expert Writers

or