- Class Number 7432
- Term Code 3060
- Class Info
- Unit Value 6 units
- Mode of Delivery In Person
- Prof Ross Maller
- Prof Ross Maller
- Class Dates
- Class Start Date 27/07/2020
- Class End Date 30/10/2020
- Census Date 31/08/2020
- Last Date to Enrol 03/08/2020
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.
Upon successful completion, students will have the knowledge and skills to:
- Use Brownian motion, martingales and Ito's formula.
- Use alternatives to Black-Scholes models such as local volatility, jump diffusion and GARCH models.
- 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.
- Value options on correlated assets, including the mathematical/stochastic foundations necessary.
- Demonstrate an understanding of the theory and use of early exercise options, including the use of optimal stopping theory.
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
No written material or formula sheets may be taken into the final exam. Further information will be announced in class and on Wattle. Students will have an opportunity to practice use of any required software or packages.
Course materials will be made available on Wattle.
- 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. The availability of an e-book copy of the textbook is still being investigated.
A digital version of Hull is 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.
- 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.
Students will be given feedback in the following forms in this course:
- feedback from Assignments 1 and 2, and the Mid Semseter Exam,
- weekly feedback from tutors during tutorials and consultation hours,
- feedback from the lecturer during consultation hours.
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.
|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 signup for this course will be done via the Wattle website. Detailed information about signup times will be provided on Wattle. When tutorials are available for enrolment, follow these steps:
1. Log on to Wattle, and go to the course site
2. Click on the link “Tutorial enrolment”
3. On the right of the screen, click on the tab “Become Member of…..” for the tutorial class you wish to enter
4. Confirm your choice
If you need to change your enrolment, you will be able to do so by clicking on the tab “Leave group….” and then re-enrol in another group. You will not be able to enrol in groups that have reached their maximum number. Please note that enrolment in ISIS must be finalised for you to have access to Wattle.
|Assessment task||Value||Due Date||Return of assessment||Learning Outcomes|
|Assignment 1||5 %||14/08/2020||30/08/2020||1, 3, 5|
|Assignment 2||5 %||31/08/2020||12/10/2020||1, 2, 3|
|Mid Semester Exam||20 %||09/10/2020||23/10/2020||1, 3, 4, 5|
|Final Examination||70 %||05/11/2020||*||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
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:
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 ANU Online 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.
No written material or formula sheets may be taken into the Final Examination. Further information about the Final Examination will be provided in class and on Wattle closer to the exam date. 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
Learning Outcomes: 1, 3, 5
Provide detailed solutions to questions based on materials from previous weeks. You may type your answer in a type-setting software or you may hand-write parts of your answers. Please ensure that your handwriting is legible.
Assignment questions will be released 2 weeks before the due date. Assignments are due at 23:59 on the due date.
Assessment Task 2
Learning Outcomes: 1, 2, 3
Provide detailed solutions to questions based on materials from previous weeks. For details, see Assessment Task 1.
Assignment questions will be released 2 weeks before the due date. Assignments are due at 23:59 on the due date.
Assessment Task 3
Learning Outcomes: 1, 3, 4, 5
Mid Semester Exam
The Mid Semester Exam is redeemable, meaning that if it is not attempted the weighting of 20% will be added to the Final Exam. No written material or formula sheets may be taken into the Mid Semester Exam. Further information about the Mid Semester Exam will be provided in class and on Wattle on later than Week 4. Centrally scheduled examinations through Examinations, Graduations & Prizes will be timetabled prior to the examination period. Please check ANU Timetabling for further information.
Assessment Task 4
Learning Outcomes: 1, 2, 3, 4, 5
No written material or formula sheets may be taken into the Final Examination. Further information about the Final Examination will be provided in class and on Wattle no later than Week 10. Centrally scheduled examinations through Examinations, Graduations & Prizes will be timetabled prior to the examination period. Please check ANU Timetabling for further information.
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.
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.
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.
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 0 will be awarded.
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.
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. The Course Convener may grant extensions 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.
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
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- ANU Health, safety & wellbeing for medical services, counselling, mental health and spiritual support
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Probability, stochastic processes, statistics, and applications to mathematical finance
Prof Ross Maller