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Unit of study_

MATH4511: Arbitrage Pricing in Continuous Time

The aim of Financial Mathematics is to establish a theoretical background for building models of securities markets and provides computational techniques for pricing financial derivatives and risk assessment and mitigation. Specialists in Financial Mathematics are widely sought after by major investment banks, hedge funds and other, government and private, financial institutions worldwide. This course is foundational for honours and masters programs in Financial Mathematics. Its aim is to introduce the basic concepts and problems of securities markets and to develop theoretical frameworks and computational tools for pricing financial products and hedging the risk associated with them. This unit will focus on two ideas that are fundamental for Financial Mathematics. You will learn how the concept of arbitrage and the concept of martingale measure provide a unified approach to a large variety of seemingly unrelated problems arising in practice. You will also learn how to use the wide range of tools required by Financial Mathematics, including stochastic calculus, partial differential equations, optimisation and statistics. By doing this unit, you will learn how to formulate problems that arise in finance as mathematical problems and how to solve them using the concepts of arbitrage and martingale measure. You will also learn how to choose an appropriate computational method and devise explicit numerical algorithms useful for a practitioner.

Details

Academic unit Mathematics and Statistics Academic Operations
Unit code MATH4511
Unit name Arbitrage Pricing in Continuous Time
Session, year
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Semester 1, 2020
Attendance mode Normal day
Location Camperdown/Darlington, Sydney
Credit points 6

Enrolment rules

Prohibitions
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None
Prerequisites
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None
Corequisites
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None
Assumed knowledge
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Familiarity with basic probability (eg STAT2X11), with differential equations (eg MATH3X63, MATH3X78) and with basic numerical analysis and coding (eg MATH3X76), achievement at credit level or above in MATH3XXX or STAT3XXX units or equivalent.

Available to study abroad and exchange students

Yes

Teaching staff and contact details

Coordinator Zhou Zhou, zhou.zhou@sydney.edu.au
Lecturer(s) Zhou Zhou , zhou.zhou@sydney.edu.au
Type Description Weight Due Length
Assignment Assignment 1
Written assessment for mathematical calculation/proof.
10% Week 05
Due date: 25 Mar 2020
1 week
Outcomes assessed: LO1 LO5 LO4 LO3 LO2
Assignment Assignment 2
Written assignment for mathematical calculation/proof.
10% Week 08
Due date: 22 Apr 2020
1 week
Outcomes assessed: LO1 LO2 LO3 LO4 LO5
Assignment Assignment 3
Written assignment for mathematical calculation/proof.
10% Week 12
Due date: 20 May 2020
1 week
Outcomes assessed: LO1 LO2 LO3 LO4 LO5
Final exam Math4511 Exam
Written exam for mathematical calculation/proof.
70% Week 13 2 hours
Outcomes assessed: LO1 LO2 LO3 LO4 LO5

Assessment will be based on the completeness and coherence of the solutions.

Assessment criteria

Assessment grading

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

Description

High distinction

85 - 100

 

Distinction

75 - 84

 

Credit

65 - 74

 

Pass

50 - 64

 

Fail

0 - 49

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

For more information see sydney.edu.au/students/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:

Late submission is not permitted, except for approaved special consideration.

Special consideration

If you experience short-term circumstances beyond your control, such as illness, injury or misadventure or if you have essential commitments which impact your preparation or performance in an assessment, you may be eligible for special consideration or special arrangements.

Academic integrity

The Current Student website provides information on academic honesty, academic dishonesty, 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 dishonesty or plagiarism seriously.

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

WK Topic Learning activity Learning outcomes
Multiple weeks Black-Sholdes model Lecture and tutorial (12 hr) LO1 LO2 LO3 LO4 LO5
Fundamental theorem of asset pricing and Martingale approach Lecture and tutorial (14 hr) LO1 LO2 LO3 LO4 LO5
Incomplete market and currency derivatives Lecture and tutorial (8 hr) LO1 LO2 LO3 LO4 LO5
Optimal stopping theory and American options Lecture and tutorial (8 hr) LO1 LO2 LO3 LO4 LO5
Extensions of Black-Scholes model Lecture and tutorial (8 hr) LO1 LO2 LO3 LO4 LO5

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.

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 a coherent and advanced knowledge of the concept of arbitrage and martingale measure and how they provide a unified approach to a wide variety of problems in finance
  • LO2. Formulate real-world financial problems in mathematical terms and determine the most suitable framework to analyse the resulting mathematical problem
  • LO3. Generate analytic and computational solutions to diverse problems of finance
  • LO4. Communicate mathematical analyses and solutions to mathematical and practical problems of financial mathematics clearly in a variety of media to diverse audiences
  • LO5. Take responsibility for their own learning by seeking out and using material from the research literature and elsewhere to extend their knowledge of methods of financial mathematics

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
GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9
This is the first time this unit has been offered.

Disclaimer

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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