Discrete Time Financial Modelling
Term 1, 2023
Cricos Provider Code: 00098G
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Staff
Position Name Email Room
Lecturer-in-charge Dr Donna Salopek dm.salopek@unsw.edu.au RC-1030
Please refer to your Timetable on MyUNSW for your Lecture/Seminar Tut, Lab enrolment days and
times. Timetable weblink: http://timetable.unsw.edu.au/2023/MATH5965.html
Administrative Contacts
Please visit the School of Mathematics and Statistics website for a range of information on School
Policies, Forms and Help for Students.
For information on Courses, please go to “Current Students” and either Undergraduate and/or
Postgraduate”, Course Homepage” for information on all course offerings,
The “Student Notice Board” can be located by going to the “Current Students” page; Notices are
posted regularly for your information here. Please familiarise yourself with the information found
in these locations. The School web page is: https://www.maths.unsw.edu.au
If you cannot find the answer to your queries on the web you are welcome to contact the Student
Services Office directly.
By email Postgraduate pg.mathsstats@unsw.edu.au
By phone: 9385 7053
Should we need to contact you, we will use your official UNSW email address of in the first
instance. It is your responsibility to regularly check your university email account. Please state
your student number in all emails.
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Course Information
We are aware some course exclusions on the Handbook may be different to the School website.
We are in the process of updating this information. Meanwhile, students should be following the
Handbook course information with the School website information as a supplement.
Course Aims
The course provides an overview of the most important classes of financial contracts that are
traded either on exchanges or over the counter between financial institutions and their clients. In
particular, options of European and American style, futures contracts and forward contracts are
discussed. We introduce the basic ideas of arbitrage pricing within the set-up of a one-period
model. In the next step, we analyse the valuation and hedging of European and American options
and general contingent claims in the framework of the classic Cox-Ross-Rubinstein binomial
model of the stock price. Finally, a general theory of arbitrage free discrete time models of spot
and futures markets is presented.
We prove the so-called Fundamental Theorems of Asset Pricing (FTAP) for a finite model of
security markets. The first FTAP establishes the equivalence between the no-arbitrage property of
a security market model and the existence of a martingale probability measure. The second FTAP
shows that the model completeness can be characterised in terms of the uniqueness of a
martingale probability measure.
Course Description
The course provides an overview of the most important classes of financial contracts that are
traded either on exchanges of over-the counter between financial institutions and their clients. We
discuss option of European and American style, futures contracts and forward contracts. The
basic ideas of arbitrage pricing are studied in the framework of the classical Cox-Ross-Rubinstein
binominal model of stock price.
Subsequently, we analyse the valuation and hedging of European and American options and
general contingent claims. We also prove the so-called fundamental theorems of asset pricing for
finite models of security markets which furnish a theoretical underpinning of the modern theory of
derivatives pricing in stochastic models of security markets.
Assessment and Deadlines
Assessment Week Weighting
%
Course Learning
Outcome (CLO)
Assignment 1: individual, Moodle Quiz Week 3 10% CLO2,
CL03
Assignment 2: Group work Week 7 15% ALL
Assignment 3: Group work Week 10 15% ALL
Final exam 60% ALL
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Late Submission of Assessment Tasks
A late penalty of 5% of the awarded mark will be applied per day or part day any assessment task
is submitted more than 1 hour late. (Where "late" in this context means after any extensions
granted for Special Consideration or Equitable Learning Provisions.) For example, an assessment
task that was awarded 75% would be given 65% if it was 1-2 days late. Any assessment task
submitted 7 or more days late will be given zero.
Note that the penalty does not apply to
Assessment tasks worth less than 5% of the total course mark, e.g. weekly quizzes,
weekly class participation, or weekly homework tasks.
Examinations and examination-style class tests
Pass/Fail Assessments
Course Learning Outcomes (CLO)
Recognise which analysis procedure is appropriate for a given research problem.
Apply probability theory and stochastic analysis to practical problems.
Understand the usefulness of probability and stochastic analysis in your professional area.
Course Schedule
The course will include material taken from some of the following topics. This is should only serve
as a guide as it is not an extensive list of the material to be covered and the timings are
approximate. The course content is ultimately defined by the material covered in lectures.
Weeks Topic Reading (if
applicable)
1 Introduction to Financial Derivatives and Probability
Refer to Moodle
Lecture notes
2 The Markov Property; Binomial Model Pricing and Hedging;
and Application to Exotic Options; Stopping Times and
American Options
3 State Prices and The Cox-Ross-Rubinstein Model
4 Security Markets in Discrete-Time
5 Random Walk; First Passage Times; Reflection Principle;
Perpetual American Options
7 Applications to pricing Barrier options and Lookback options
8 Special topic - TBA
9 Special topic - TBA
10 Special topic - TBA
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Suggested Textbooks
Steven E. Shreve: Stochastic Calculus for Finance I. The Binomial Asset
Pricing Model. Springer, 2004.
Stanley R. Pliska: Introduction to Mathematical Finance: Discrete Time Models.
Blackwell Publishers, Oxford, 1997.
Marek Musiela and Marek Rutkowski: Martingale Methods in Financial Modelling.
Springer-Verlag, Berlin Heidelberg New York, Second edition, 2005.
John C. Hull: Options, Futures, and Other Derivatives. Prentice-Hall, Englewood Cliffs,
1997.
Martin W. Baxter and Andrew Rennie: Financial Calculus. An Introduction to Derivative
Pricing. Cambridge University Press, Cambridge, 1997.
Hans Foellmer and Alexander Schied: Stochastic Finance: An Introduction in Discrete
Time. De Gruyter, 2000.
Nicholas Privault, Introduction to Stochastic Finances with Market Examples. Chapman and
Hall, 2022
Moodle
Log in to Moodle to find announcements, general information, notes, lecture slide, classroom tutorial
and assessments etc.
https://moodle.telt.unsw.edu.au
School and UNSW Policies
The School of Mathematics and Statistics has adopted a number of policies relating to enrolment,
attendance, assessment, plagiarism, cheating, special consideration etc. These are in addition to
the Policies of The University of New South Wales. Individual courses may also adopt other
policies in addition to or replacing some of the School ones. These will be clearly notified in the
Course Initial Handout and on the Course Home Pages on the Maths Stats web site.
Students in courses run by the School of Mathematics and Statistics should be aware of the School
and Course policies by reading the appropriate pages on the Maths Stats web site starting at:
https://www.maths.unsw.edu.au/currentstudents/assessment-policies
The School of Mathematics and Statistics will assume that all its students have read and
understood the School policies on the above pages and any individual course policies on the
Course Initial Handout and Course Home Page. Lack of knowledge about a policy will not be an
excuse for failing to follow the procedure in it.
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Academic Integrity and Plagiarism
UNSW has an ongoing commitment to fostering a culture of learning informed by academic
integrity. All UNSW staff and students have a responsibility to adhere to this principle of academic
integrity. Plagiarism undermines academic integrity and is not tolerated at UNSW. Plagiarism at
UNSW is defined as using the words or ideas of others and passing them off as your own.
The UNSW Student Code provides a framework for the standard of conduct expected of UNSW
students with respect to their academic integrity and behaviour. It outlines the primary
obligations of students and directs staff and students to the Code and related procedures.
In addition, it is important that students understand that it is not permissible to buy
essay/writing services from third parties as the use of such services constitutes plagiarism
because it involves using the words or ideas of others and passing them off as your own. Nor is
it permissible to sell copies of lecture or tutorial notes as students do not own the rights to this
intellectual property.
If a student breaches the Student Code with respect to academic integrity, the University may take
disciplinary action under the Student Misconduct Procedure.
The UNSW Student Code and the Student Misconduct Procedure can be found at:
https://student.unsw.edu.au/plagiarism
An online Module “Working with Academic Integrity” (https://student.unsw.edu.au/aim) is a six-
lesson interactive self-paced Moodle module exploring and explaining all of these terms and
placing them into your learning context. It will be the best one-hour investment you’ve ever made.
Plagiarism
Plagiarism is presenting another person's work or ideas as your own. Plagiarism is a serious
breach of ethics at UNSW and is not taken lightly. So how do you avoid it? A one-minute video for
an overview of how you can avoid plagiarism can be found
https://student.unsw.edu.au/plagiarism.
Additional Support
ELISE (Enabling Library and Information Skills for Everyone)
ELISE is designed to introduce new students to studying at UNSW.
Completing the ELISE tutorial and quiz will enable you to:
analyse topics, plan responses and organise research for academic writing and other
assessment tasks
effectively and efficiently find appropriate information sources and evaluate relevance
to your needs
use and manage information effectively to accomplish a specific purpose
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better manage your time
understand your rights and responsibilities as a student at UNSW
be aware of plagiarism, copyright, UNSW Student Code of Conduct and Acceptable Use of
UNSW ICT Resources Policy
be aware of the standards of behaviour expected of everyone in the UNSW community
locate services and information about UNSW and UNSW Library
Some of these areas will be familiar to you, others will be new. Gaining a solid understanding of all
the related aspects of ELISE will help you make the most of your studies at UNSW.
The ELISE training webpages:
https://subjectguides.library.unsw.edu.au/elise/aboutelise
Equitable Learning Services (ELS)
If you suffer from a chronic or ongoing illness that has, or is likely to, put you at a serious
disadvantage, then you should contact the Equitable Learning Services (previously known as
SEADU) who provide confidential support and advice.
They assist students:
living with disabilities
with long- or short-term health concerns and/or mental health issues
who are primary carers
from low SES backgrounds
of diverse genders, sexes and sexualities
from refugee and refugee-like backgrounds
from rural and remote backgrounds
who are the first in their family to undertake a bachelor-level degree.
Their web site is: https://student.unsw.edu.au/els/services
Equitable Learning Services (ELS) may determine that your condition requires special
arrangements for assessment tasks. Once the School has been notified of these, we will make
every effort to meet the arrangements specified by ELS.
Additionally, if you have suffered significant misadventure that affects your ability to complete the
course, please contact your Lecturer-in-charge in the first instance.
Academic Skills Support and the Learning Centre
The Learning Centre offers academic support programs to all students at UNSW Australia. We
assist students to develop approaches to learning that will enable them to succeed in their
academic study. For further information on these programs please go to:
http://www.lc.unsw.edu.au/services-programs
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Applications for Special Consideration for Missed Assessment
Please adhere to the Special Consideration Policy and Procedures provided on the web page below
when applying for special consideration.
https://student.unsw.edu.au/special-consideration
Please note that the application is not considered by the Course Authority, it is considered by a
centralised team of staff at the Nucleus Student Hub.
The School will contact you (via student email account) after special consideration has been
granted to reschedule your missed assessment, for a lab test or paper-based test only.
For applications for special consideration for assignment extensions, please note that the new
submission date and/or outcome will be communicated through the special consideration web site
only, no communication will be received from the School.
For Dates on Final Term Exams and Supplementary Exams please check the “Key Dates for Exams”
ahead of time to avoid booking holidays or work obligations.
https://student.unsw.edu.au/exam-dates
If you believe your application for Special Consideration has not been processed, you should email
specialconsideration@unsw.edu.au immediately for advice.
Course Evaluation and Development (MyExperience)
Student feedback is very important to continual course improvement. This is demonstrated within
the School of Mathematics and Statistics by the implementation of the UNSW online student
survey myExperience, which allows students to evaluate their learning experiences in an
anonymous way. myExperience survey reports are produced for each survey. They are released to
staff after all student assessment results are finalised and released to students. Course convenor
will use the feedback to make ongoing improvements to the course.