• Class Number 6972
• Term Code 3360
• Class Info
• Unit Value 6 units
• Mode of Delivery In Person
• COURSE CONVENER
• Dr Kevin Lu
• LECTURER
• Dr Kevin Lu
• Class Dates
• Class Start Date 24/07/2023
• Class End Date 27/10/2023
• Census Date 31/08/2023
• Last Date to Enrol 31/07/2023
SELT Survey Results

Advanced Derivatives Pricing and Applications (FINM3007)

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

Exams will be in-person and closed-book. No written material or formula sheets may be taken into the final exam. Further information will be announced in class and on Wattle.

## Required Resources

Course materials will be made available on Wattle.

Prescribed Texts:

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 as a reference for the course content in Weeks 1, 4-12. Bingham and Kiesel will be used as a reference for the course content in Weeks 2-3, and is also useful as an additional reference for content in Weeks 4, 9, 12.

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). Feedback can also be provided to Course Conveners and teachers via the Student Experience of Learning & Teaching (SELT) feedback program. SELT surveys are confidential and also provide the Colleges and ANU Executive with opportunities to recognise excellent teaching, and opportunities for improvement.

## Class Schedule

Week/Session Summary of Activities Assessment
1 Derivative pricing review, dividends and American options
2 Martingales, Snell envelope and optimal stopping
3 Applications of optimal stopping to American options
4 Change of numeraire, change of measure Assignment 1 due
5 Bivariate GBM, derivatives on 2 assets, compound options
6 Binomial pyramid, quantos
7 Imperfections of the BS model, implied risk-neutral distributions, local volatility models Mid-semester exam
8 Jump-diffusion models, variance gamma models
9 Levy processes, Esscher transforms
10 Stochastic volatility with GARCH and Heston models Assignment 2 due
11 Value-at-risk using EVT and POT methods
12 Credit risk, Merton's model for default, credit default swaps, revision

## Tutorial Registration

Students should enrol in their tutorial using MyTimetable.

## Assessment Summary

Assessment task Value Due Date Return of assessment Learning Outcomes
Assignment 1 5 % 18/08/2023 30/08/2023 1, 3, 5
Mid-semester Examination 20 % 18/09/2023 06/10/2023 1, 3, 4, 5
Assignment 2 5 % 13/10/2023 27/10/2023 1, 2, 3
Final Examination 70 % 02/11/2023 30/11/2023 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 Integrity Rule before the commencement of their course. Other key policies and guidelines include:

## 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 Skills website. 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 delivered in-person, on-campus, and recorded via Echo 360. Tutorials will be delivered in-person and on-campus. 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.

Value: 5 %
Due Date: 18/08/2023
Return of Assessment: 30/08/2023
Learning Outcomes: 1, 3, 5

Assignment 1

Provide answers to questions based on materials in previous weeks. You may type or handwrite your answers. Assignments will be submitted using TurnItIn/Wattle. The 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.

Value: 20 %
Due Date: 18/09/2023
Return of Assessment: 06/10/2023
Learning Outcomes: 1, 3, 4, 5

Mid-semester Examination

The mid-semester exam will be in-person and closed-book with 1 hour and 30 minutes writing time. It will be held in the consecutive lecture and tutorial timeslot in Thursday Week 7. The mid-semester exam is redeemable, meaning that if it is not attempted the weighting will be added to the final exam. Further information will be provided by Week 5.

Value: 5 %
Due Date: 13/10/2023
Return of Assessment: 27/10/2023
Learning Outcomes: 1, 2, 3

Assignment 2

Provide answers to questions based on materials in previous weeks. You may type or handwrite your answers. Assignments will be submitted using TurnItIn/Wattle. The 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.

Value: 70 %
Due Date: 02/11/2023
Return of Assessment: 30/11/2023
Learning Outcomes: 1, 2, 3, 4, 5

Final Examination

The final exam will be in-person and closed-book with 3 hours writing time. Further information other than timetabling will be provided by Week 10. The exam will be centrally timetabled and details of the final examination timetable will be made available on the ANU timetabling website.

Academic integrity is a core part of the ANU culture as a community of scholars. The University’s students are an integral part of that community. The academic integrity principle commits all students to engage in academic work in ways that are consistent with, and actively support, academic integrity, and to uphold this commitment by behaving honestly, responsibly and ethically, and with respect and fairness, in scholarly practice.

The University expects all staff and students to be familiar with the academic integrity principle, the Academic Integrity Rule 2021, the Policy: Student Academic Integrity and Procedure: Student Academic Integrity, and to uphold high standards of academic integrity to ensure the quality and value of our qualifications.

The Academic Integrity Rule 2021 is a legal document that the University uses to promote academic integrity, and manage breaches of the academic integrity principle. The Policy and Procedure support the Rule by outlining overarching principles, responsibilities and processes. The Academic Integrity Rule 2021 commences on 1 December 2021 and applies to courses commencing on or after that date, as well as to research conduct occurring on or after that date. Prior to this, the Academic Misconduct Rule 2015 applies.

The University commits to assisting all students to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. All coursework students must complete the online Academic Integrity Module (Epigeum), and Higher Degree Research (HDR) students are required to complete research integrity training. The Academic Integrity website provides information about services available to assist students with their assignments, examinations and other learning activities, as well as understanding and upholding academic integrity.

## 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

The Academic Skills website has information to assist you with your writing and assessments. The website includes information about Academic Integrity including referencing requirements for different disciplines. There is also information on Plagiarism and different ways to use source material.

## 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.
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.

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).

## Convener

 Dr Kevin Lu kevin.lu@anu.edu.au

### Research Interests

Probability, stochastic processes, statistics, and applications to mathematical finance

### Dr Kevin Lu

 Tuesday 15:00 16:00 Tuesday 15:00 16:00

## Instructor

 Dr Kevin Lu 6125 6710 kevin.lu@anu.edu.au

### Dr Kevin Lu

 Tuesday 15:00 16:00 Tuesday 15:00 16:00