This is an advanced course in derivatives pricing and hedging, and their applications. The aim is to cover topics such as: advanced features of the Black-Scholes model, including exotic options and derivatives dependent on the same Brownian motion; some bivariate/multivariate theory (normal distribution, Brownian motion in 2 dimensions), as needed for pricing options on correlated assets; Rubinstein's binomial pyramid for approximating a bivariate GBM; change of numeraire and equivalent martingale measures; optimal stopping theory as needed for American option pricing; hedging concepts in this context; alternatives to Black-Scholes models; local volatility models, jump diffusion and GARCH models. There will be an emphasis on early exercise options, and some time will be spent on the mathematical/stochastic foundations necessary for understanding these and other applications. Some Value-at-Risk concepts may be introduced, and applied to portfolios containing derivatives. Credit derivatives may also be discussed.

Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

1. Use Brownian motion, martingales and Ito's formula.
2. Use alternatives to Black-Scholes models such as local volatility, jump diffusion and GARCH models.
3. Apply the arbitrage-free approach to the pricing of options, including exotic options, using the basic mathematical tools required, and demonstrate an understanding of how these options are used in financial practice.
4. Value options on correlated assets, including the mathematical/stochastic foundations necessary.
5. Demonstrate an understanding of the theory and use of early exercise options, including the use of optimal stopping theory.

Research-Led Teaching

ANU has a rich history of research in the area of stochastic processes relating to derivative pricing. The lecturer and other RSFAS staff members are active researchers in this area, with a keen interest to attract talented students for research projects.

Examination Material or equipment

The final exam will be open book. Further information will be announced in class and on Wattle. Students will have an opportunity to practice use of any required software or packages.

Required Resources

Course materials will be made available on Wattle.

Prescribed Texts:

• Options, Futures, and Other Derivatives, J. Hull, Pearson, Global Edition, 8 or 9e, 2012 or 2018.
• Risk Neutral Valuation, N. Bingham and R. Kiesel, Springer, 2004.

A digital version of Hull and of Bingham and Kiesel are available from the ANU Library. Physical copies of both textbooks are on 2 hour reserve at the Chifley Library. Hull will be used a reference for the course content in Weeks 1, 4-12. Bingham and Kiesel will be used a reference for the course content in Weeks 2-3.

Recommended Resources

Books:

• Introduction to Stochastic Calculus with Applications., F. Klebaner, Imp. Coll. Press, 1998.
• Elementary Stochastic Calculus with Finance in View, T. Mikosch, World Scientific, 1998.
• Financial Calculus, M.W. Baxter and A.J.O. Rennie, Cambridge Univ. Press, 1996.
• Options Markets, J. C. Cox and Mark Rubinstein, Prentice-Hall, 1985.
• Value at Risk: the New Benchmark for Managing Financial Risk, P. Jorion, 2e, McGraw-Hill, 2001. 
• Levy Processes in Finance: Pricing Financial Derivatives, W. Schoutens, Wiley, 2003.

The first 5 books in this list are available from the ANU Library. Parts of these books may be a useful reference for some topics in the course or for further reading beyond the course content. They are additional material and not necessary for completing the course.

Staff Feedback

Students will be given feedback in the following forms in this course:

• feedback from Assignments 1 and 2, and the mid-semester exam,
• weekly feedback from tutors during tutorials and consultation hours,
• feedback from the lecturer during consultation hours.

Student Feedback

ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. The Surveys and Evaluation website provides more information on student surveys at ANU and reports on the feedback provided on ANU courses.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Review of the continuous time market model; dividends and American options: critical price, Hull's approximation
2	Review of martingales; Snell envelope and optimal stopping
3	Application of optimal stopping to American options
4	Change of numeraire, derivatives dependent on the same BM, option to exchange assets	Assignment 1 due
5	Black's model, bivariate GBM, derivatives on 2 assets
6	Compound options, quantos, Siegel's paradox, binomial pyramid
7	Alternatives to BS: local volatility, Dupire's formula, jump diffusion models	Mid-semester exam
8	Variance gamma models
9	GARCH and CEV models
10	Heston model, Merton's model for default	Assignment 2 due
11	Value-at-risk using EVT and POT methods
12	Credit risk, revision

Tutorial Registration

Tutorials will be available on campus, live through scheduled Zoom sessions and as pre-recorded videos. Students should enrol in their tutorial using MyTimetable.  

"ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage (https://www.anu.edu.au/students/program-administration/timetabling)".

 

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Assignment 1	5 %	19/08/2022	02/09/2022	1, 3, 5
Assignment 2	5 %	14/10/2022	28/10/2022	1, 2, 3
Mid-semester Examination	20 %	19/09/2022	07/10/2022	1, 3, 4, 5
Final Examination	70 %	03/11/2022	02/12/2022	1, 2, 3, 4, 5

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

Policies

ANU has educational policies, procedures and guidelines, which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Misconduct Rule before the commencement of their course. Other key policies and guidelines include:

• Student Assessment (Coursework) Policy and Procedure
• Special Assessment Consideration Policy and General Information 
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure

Assessment Requirements

The ANU is using Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. For additional information regarding Turnitin please visit the Academic Integrity . In rare cases where online submission using Turnitin software is not technically possible; or where not using Turnitin software has been justified by the Course Convener and approved by the Associate Dean (Education) on the basis of the teaching model being employed; students shall submit assessment online via ‘Wattle’ outside of Turnitin, or failing that in hard copy, or through a combination of submission methods as approved by the Associate Dean (Education). The submission method is detailed below.

Moderation of Assessment

Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.

Participation

Lectures will be both live and recorded via Echo 360; tutorials will be available both face-to-face and via Zoom. Students will be able to engage with the lecturer and tutor(s) during weekly consultations, which will be held via Zoom. Comments on the discussion board will be monitored and responded to as appropriate.

Examination(s)

Centrally scheduled examinations through Examinations, Graduations & Prizes will be timetabled prior to the examination period. Please check ANU Timetabling for further information.

Assessment Task 1

Assignment 1

Provide detailed solutions to questions based on materials from Weeks 1 to 4. You may type your answers using typesetting software or you may hand-write your answers. Please ensure that your handwriting is legible. Your answers are to be submitted in Turnitin/Wattle via the assignment submission link. This assignment is to be completed individually.

Assignment questions will be released 2 weeks before the due date. Assignments are due at 23:59 on the due date.

Assessment Task 2

Assignment 2

Provide detailed solutions to questions based on materials from Weeks 1 to 10. You may type your answers using typesetting software or you may hand-write your answers. Please ensure that your handwriting is legible. Your answers are to be submitted in Turnitin/Wattle via the assignment submission link. This assignment is to be completed individually.

Assignment questions will be released 2 weeks before the due date. Assignments are due at 23:59 on the due date.

Assessment Task 3

Mid-semester Examination

The mid-semester examination will be a Wattle-based online exam (2.5-hour writing time) that will be held during the university mid-semester examination period. It will be an open book exam. Students will be provided with further details regarding the exam as it approaches. Students will have an opportunity to practice use of any required software or packages. The exam will be centrally timetabled and details of the mid-semester examination timetable will be made available on the ANU timetabling website. It will be worth 20% of the overall mark.

Assessment Task 4

Final Examination

The final examination will be a Wattle-based online exam (3.5-hour writing time) that will be held during the university examination period at the end of the semester. It will be an open book exam. Students will be provided with further details regarding the exam as it approaches (no later than week 10). Students will have an opportunity to practice use of any required software or packages. The exam will be centrally timetabled and details of the final examination timetable will be made available on the ANU timetabling website. It will be worth 70% of the overall mark.

 

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. At its heart, academic integrity is about behaving ethically, committing to honest and responsible scholarly practice and upholding these values with respect and fairness.

The ANU commits to assisting all members of our community to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. The ANU expects staff and students to be familiar with the academic integrity principle and Academic Misconduct Rule, uphold high standards of academic integrity and act ethically and honestly, to ensure the quality and value of the qualification that you will graduate with.

The Academic Misconduct Rule is in place to promote academic integrity and manage academic misconduct. Very minor breaches of the academic integrity principle may result in a reduction of marks of up to 10% of the total marks available for the assessment. The ANU offers a number of online and in person services to assist students with their assignments, examinations, and other learning activities. Visit the Academic Skills website for more information about academic integrity, your responsibilities and for assistance with your assignments, writing skills and study.

Online Submission

You will be required to electronically sign a declaration as part of the submission of your assignment. Please keep a copy of the assignment for your records. Unless an exemption has been approved by the Associate Dean (Education) submission must be through Turnitin.

Hardcopy Submission

For some forms of assessment (hand written assignments, art works, laboratory notes, etc.) hard copy submission is appropriate when approved by the Associate Dean (Education). Hard copy submissions must utilise the Assignment Cover Sheet. Please keep a copy of tasks completed for your records.

Late Submission

No submission of assignments without an extension after the due date will be permitted. If an assignment is not submitted by the due date, a mark of zero will be awarded.

Referencing Requirements

Accepted academic practice for referencing sources that you use in presentations can be found via the links on the Wattle site, under the file named “ANU and College Policies, Program Information, Student Support Services and Assessment”. Alternatively, you can seek help through the Students Learning Development website.

Returning Assignments

Assignments will be graded and returned on Wattle via TurnitIn.

Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure. Extensions may be granted for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.

Resubmission of Assignments

No resubmission of assignments is permitted.

Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information.
In cases where student end users are asked to submit ‘content’ to a database, such as an assignment or short answers, the database licensor may only use the student’s ‘content’ in accordance with the terms of service – including any (copyright) licence the student grants to the database licensor. Any personal information or content a student submits may be stored by the licensor, potentially offshore, and will be used to process the database service in accordance with the licensors terms of service and/or privacy policy.
If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

Distribution of grades policy

Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes.

Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.

Support for students

The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).

• ANU Health, safety & wellbeing for medical services, counselling, mental health and spiritual support
• ANU Diversity and inclusion for students with a disability or ongoing or chronic illness
• ANU Dean of Students for confidential, impartial advice and help to resolve problems between students and the academic or administrative areas of the University
• ANU Academic Skills and Learning Centre supports you make your own decisions about how you learn and manage your workload.
• ANU Counselling Centre promotes, supports and enhances mental health and wellbeing within the University student community.
• ANUSA supports and represents undergraduate and ANU College students
• PARSA supports and represents postgraduate and research students