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Unit outline_

MATH3975: Financial Derivatives (Advanced)

Semester 2, 2023 [Normal day] - Camperdown/Darlington, Sydney

This unit will introduce you to the mathematical theory of modern finance with the special emphasis on the valuation and hedging of financial derivatives, such as: forward contracts and options of European and American style. You will learn about the concept of arbitrage and how to model risk-free and risky securities. Topics covered by this unit include: the notions of a martingale and a martingale measure, the fundamental theorems of asset pricing, complete and incomplete markets, the binomial options pricing model, discrete random walks and the Brownian motion, the Black-Scholes options pricing model and the valuation and hedging of exotic options. Students completing this unit have been highly sought by the finance industry, which continues to need graduates with quantitative skills. Students enrolled in this unit at advanced level will have to undertake more challenging assessment tasks, but lectures in the advanced level are held concurrently with those of the corresponding mainstream unit.

Unit details and rules

Academic unit Mathematics and Statistics Academic Operations
Credit points 6
A mark of 65 or above in 12cp from (MATH2XXX or STAT2XXX or DATA2X02)
MATH3933 or MATH3015 or MATH3075
Assumed knowledge


Available to study abroad and exchange students


Teaching staff

Coordinator Marek Rutkowski,
Lecturer(s) Marek Rutkowski,
Type Description Weight Due Length
Supervised exam
Final examination
4 problem based questions
60% Formal exam period 2 hours
Outcomes assessed: LO1 LO2 LO3 LO4 LO6 LO7
Assignment Assignment 1
Problem based questions
20% Week 06
Due date: 10 Sep 2023 at 23:59

Closing date: 17 Sep 2023
2 weeks
Outcomes assessed: LO1 LO2 LO3
Assignment Assignment 2
Problem based questions
20% Week 11
Due date: 22 Oct 2023 at 23:59

Closing date: 29 Oct 2023
2 weeks
Outcomes assessed: LO4 LO5 LO6 LO7

Assessment summary

Detailed information for each assessment can be found on Canvas. If a second replacement exam is required, this exam may be delivered via an alternative assessment method, such as viva voce (oral exam). The alternative assessment will meet the same learning outcomes as the original exam. The formal of the alternative assessment will be determined by the unit coordinator.

Assessment criteria

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

As a general guide, a high distinction indicates work of an exceptional standard, a distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

Result name

Mark range


High distinction

85 - 100

Representing complete or close to complete mastery of the material.


75 - 84

Representing excellence, but substantially less than complete mastery.


65 - 74

Representing a creditable performance that goes beyond routine knowledge and understanding, but less than excellence.


50 - 64

Representing at least routine knowledge and understanding over a spectrum of topics and important ideas and concepts in the course.


0 - 49

When you don’t meet the learning outcomes of the unit to a satisfactory standard.

For more information see guide to grades.

Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

  • Deduction of 5% of the maximum mark for each calendar day after the due date.
  • After ten calendar days late, a mark of zero will be awarded.

This unit has an exception to the standard University policy or supplementary information has been provided by the unit coordinator. This information is displayed below:

For every calendar date up to and including ten calendar days after the due date, a penalty of 5% of the maximum awardable marks will be applied to late work. For work submitted more than ten days after the due date a mark of zero will be awarded.

Academic integrity

The Current Student website  provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.  

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.

Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.

Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

WK Topic Learning activity Learning outcomes
Week 01 Overview of probability Lecture and tutorial (4 hr) LO1
Week 02 Introduction to financial markets Lecture and tutorial (4 hr) LO1
Week 03 Two-state single-period market models Lecture and tutorial (4 hr) LO2
Week 04 General single-period market models Lecture and tutorial (4 hr) LO2 LO3
Week 05 Proof of the fundamental theorem of asset pricing Lecture and tutorial (4 hr) LO2 LO3
Week 06 Completeness of single-period models Lecture and tutorial (4 hr) LO2 LO3
Week 07 General multi-period market models Lecture and tutorial (4 hr) LO2 LO3
Week 08 Filtrations, martingales and martingale measures Lecture and tutorial (4 hr) LO2 LO3
Week 09 The Cox-Ross-Rubinstein (CRR) market model Lecture and tutorial (4 hr) LO2 LO3
Week 10 American and game options in the CRR model Lecture and tutorial (4 hr) LO4 LO5
Week 11 Brownian motion and the Black and Scholes market model Lecture and tutorial (4 hr) LO6 LO7
Week 12 Black-Scholes options pricing formula and PDE Lecture and tutorial (4 hr) LO6 LO7
Week 13 Implied volatility and sensitivities of options Block teaching (4 hr) LO6 LO7

Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

Required readings

MATH3975 Financial Derivatives (course notes on Canvas)

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

At the completion of this unit, you should be able to:

  • LO1. Demonstrate familiarity with fundamental concepts in the area of financial markets with application to existing securities related to equities and interest rates.
  • LO2. Develop stochastic models and solve qualitative and quantitative problems associated with the valuation and hedging of options.
  • LO3. Understand, explain and apply the principles of stochastic modelling in the context of financial markets.
  • LO4. Understand, explain and apply the principles of optimal stopping in the context of American-style options.
  • LO5. Understand, explain and apply the principles of Dynkin games in the context of game options.
  • LO6. Understand and apply the Black-Scholes continuous-time model for European-style options.
  • LO7. Apply mathematical expertise to solve practical problems using various approaches in discrete and continuous time.​

Graduate qualities

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

GQ1 Depth of disciplinary expertise

Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline.

GQ2 Critical thinking and problem solving

Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem.

GQ3 Oral and written communication

Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context.

GQ4 Information and digital literacy

Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies.

GQ5 Inventiveness

Generating novel ideas and solutions.

GQ6 Cultural competence

Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues.

GQ7 Interdisciplinary effectiveness

Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries.

GQ8 Integrated professional, ethical, and personal identity

An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context.

GQ9 Influence

Engaging others in a process, idea or vision.

Outcome map

Learning outcomes Graduate qualities

This section outlines changes made to this unit following staff and student reviews.

No changes have been made since this unit was last offered.

Work, health and safety

We are governed by the Work Health and Safety Act 2011, Work Health and Safety Regulation 2011 and Codes of Practice. Penalties for non-compliance have increased. Everyone has a responsibility for health and safety at work. The University’s Work Health and Safety policy explains the responsibilities and expectations of workers and others, and the procedures for managing WHS risks associated with University activities.

General laboratory safety rules

  • No eating or drinking is allowed in any laboratory under any circumstances 
  • A laboratory coat and closed-toe shoes are mandatory 
  • Follow safety instructions in your manual and posted in laboratories 
  • In case of fire, follow instructions posted outside the laboratory door 
  • First aid kits, eye wash and fire extinguishers are located in or immediately outside each laboratory 
  • As a precautionary measure, it is recommended that you have a current tetanus immunisation. This can be obtained from University Health Service:


The University reserves the right to amend units of study or no longer offer certain units, including where there are low enrolment numbers.

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