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MATH4091: Financial Calculus

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Home About this Course Course Profile Lectures Tutorials, Labs, Assignments Resources	MATH4091 Course Profile for Semester 1, 2004 (2 unit, 3L 1T) Course Objective To provide a practical introduction to some of the techniques from stochastic analysis which are applicable to finance. Contact and Advice The course coordinator, Dr Bevan Thompson, has an office 67-651 in the Priestley Building, (building 67). If you have any comments or suggestions on the course or have questions on the course material, contact the coordinator by phone on 3365 3252 or by email at hbt@maths.uq.edu.au. You are welcome to ask any questions about the course during consultation hours. If you have questions about your current or future program of study, contact the chief academic advisor, honours advisor or postgraduate advisor . Assumed Background Familiarity with calculus and probability. Concepts such as random variables, stochastic processes, expected value, variance, and conditional expectation will be discussed without detailed definition. This course has no formal prerequisites and is designed to be self-contained. It is a student's own responsibility to fill in any gaps in their assumed knowledge. You may need to undertake background reading to understand the lecture material. Teaching Mode Three hours of lectures and one hour of tutorial per week. Lectures: Tuesday 4-6pm 67-342, Wednesday 4-5pm 67-343 Tutorials: Wednesday 5-6pm 67-343 There are no tutorials in week 1 Public holidays: April 9, May 3, June 14, 2004. Midsemester Break: April 12-18, 2004. Examination period: Revision period is June 7-13, 2004. Examination period is June 15-26, 2004 Syllabus MATH4091 is mainly concerned with the pricing theory associated with derivative securities such as options. We move from a binomial stock market model to the more sophisticated continuous time models driven by Brownian motion. The focus is on developing and understanding a generalized semi-martingale market. A significant portion is devoted to background on stochastic calculus and probabilistic interpretations. Further details of contents areas will be supplied later. Information Changes Any changes to course information will be announced in lectures and the information will be reproduced on the web page http://www.maths.uq.edu.au/courses/MATH4091. It is your responsibility to keep up to date with all information presented in lectures. Resources Course Notes: There is no specified text for the course, but online lecture notes by Mark Thompson should prove useful. Notes for some sections of the course will be made available from the lecture notes page. Lecture notes must be taken in the lectures. Supplementary reading (highly recommended): A good introductory book to financial calculus and the first half of the course is: M. Baxter and A. Rennie, Financial Calculus: An Introduction to Derivative Pricing, Cambridge University Press, Cambridge, 1996. A good introductory book for the second half of the course is: F. C. Klebaner, Introduction to Stochastic Calculus with Applications, Imperial College Press, London, 1998. Advanced level books include: B. Oksendal, Stochastic Differential Equations: An Introduction with Applications, 5th edition, Springer-Verlag, New York, 1998. H. J. Kushner and P. G. Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time, Springer-Verlag, New York, 1992. Web: The course web page is at http://www.maths.uq.edu.au/courses/MATH4091. Information about the course and other resources are available there. Assessment Assessment Scheme: There will be four (4) assignments each counting ten (10) percent of the assessment and a final two (2) hour examination counting sixty (60) percent of the assessment. Submission of assignments: Assignments must be submitted in your tutorial session. Late assignments attract a 1 mark penalty for every day it is overdue. Dates for submission are Assignment 1: 17th March Assignment 2: 7th April Assignment 3: 12th May Assignment 4: 2nd June Marks are awarded for correctness and clarity of presentation. One bonus mark per assignment may be awarded for innovative solutions. Part marks will be awarded for the successful completion of subtasks. Some sample marking schemes will be distributed during the semester. If you miss an assignment: In case of illness (or bereavement) you may be exempted from an assignment if a medical certificate (or other documentation) is received by the course co-ordinator within one week of the due date of the assignment. If you are exempted, then your assignment marks are weighted on a pro-rata basis. Note that ad hoc excuses (car trouble and the like!) will not be accepted; only documentation in connection with illness or bereavement . If you enrolled late then exemption will automatically be granted for anything missed before the date of enrolment. Final Examination: The final exam is closed book 2 hours long which will be held in the examinations period at a time and place to be advised by examinations section. Calculators without ASCII capabilities are permitted. Anything discussed in lectures is examinable. In addition problems from assignments and tutorials as well as similar problems may form part of the written exam. If you miss the final exam: See the Official Examination Policies at the Resources Page http://www.maths.uq.edu.au/courses/MATH4091/Resources.html This page contains a lot of useful information about examinations as well as about available resources. Failure to complete assessment items: Failure to complete any item of assessment will result in a weighting of zero for that item except as provided for under the heading "If you miss the final exam". For information on Plagiarism, Help available for students with disabilities, University policy on Special and Supplementary Examinations, Feedback on Assessment, Assistance for students, or The student Liason Officer, visit http://spider.sps.uq.edu.au/course_profile_info.pdf Assessment Criteria: To earn a Grade of 7, a st udent must demonstrate an excellent understanding of all of the theory. This includes clear expression of nearly all their deductions and explanations, the use of appropriate and efficient mathematical techniques and accurate answers to nearly all questions and tasks with appropriate justification. To earn a Grade of 6, a student must demonstrate a comprehensive understanding of the theory of advanced analysis. This includes clear expression of most of their deductions and explanations, the general use of appropriate and efficient mathematical techniques and accurate answers to most questions and tasks with appropriate justification. To earn a Grade of 5, a student must demonstrate an adequate understanding of the course theory. This includes clear expression of some of their deductions and explanations, the use of appropriate and efficient mathematical techniques in some situations and accurate answers to some questions and tasks with appropriate justification. To earn a Grade of 4, a student must demonstrate an understanding of the basic concepts of advanced analysi s. This includes occasionally expressing their deductions and explanations clearly, the occasional use of appropriate and efficient mathematical techniques and accurate answers to a few questions and tasks with appropriate just ification. They will have demonstrated knowledge of techniques used to solve problems and applied this knowledge in some cases. To earn a Grade of 3, a student must demonstrate some knowledge of the basic concepts of advanced analysis. This includes occasional expression of their deductions and explanations, the use of a few appropriate and efficient mathematical techniques and attempts to answer a few questions and tasks accurately and with appropriate justification. They will have demonstrated knowledge of techniques used to solve problems. To earn a Grade of 2, a student must demonstrate some knowledge of the basic concepts of advanced analysis. This includes attempts at expressing their deductions and explanations and attempts to answer a few questions accurately. A student will receive a Grade of 1 if they demonstrate extremely poor knowledge of the basic concepts in the course material. This includes attempts at answering some questions but showing an extremely poor understanding of the key concepts.

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MATH4091 Course Profile for Semester 1, 2004

(2 unit, 3L 1T)

Course Objective

To provide a practical introduction to some of the techniques from stochastic analysis which are applicable to finance.

Contact and Advice

The course coordinator, Dr Bevan Thompson, has an office 67-651 in the Priestley Building, (building 67). If you have any comments or suggestions on the course or have questions on the course material, contact the coordinator by phone on 3365 3252 or by email at hbt@maths.uq.edu.au. You are welcome to ask any questions about the course during consultation hours. If you have questions about your current or future program of study, contact the chief academic advisor, honours advisor or postgraduate advisor .

Assumed Background

Familiarity with calculus and probability. Concepts such as random variables, stochastic processes, expected value, variance, and conditional expectation will be discussed without detailed definition. This course has no formal prerequisites and is designed to be self-contained. It is a student's own responsibility to fill in any gaps in their assumed knowledge. You may need to undertake background reading to understand the lecture material.

Teaching Mode

Three hours of lectures and one hour of tutorial per week.
Lectures: Tuesday 4-6pm 67-342, Wednesday 4-5pm 67-343
Tutorials: Wednesday 5-6pm 67-343
There are no tutorials in week 1
Public holidays: April 9, May 3, June 14, 2004.
Midsemester Break: April 12-18, 2004.
Examination period: Revision period is June 7-13, 2004. Examination period is June 15-26, 2004

Syllabus

MATH4091 is mainly concerned with the pricing theory associated with derivative securities such as options. We move from a binomial stock market model to the more sophisticated continuous time models driven by Brownian motion. The focus is on developing and understanding a generalized semi-martingale market. A significant portion is devoted to background on stochastic calculus and probabilistic interpretations. Further details of contents areas will be supplied later.

Information Changes

Any changes to course information will be announced in lectures and the information will be reproduced on the web page http://www.maths.uq.edu.au/courses/MATH4091. It is your responsibility to keep up to date with all information presented in lectures.

Resources

Course Notes:
There is no specified text for the course, but online lecture notes by Mark Thompson should prove useful.
Notes for some sections of the course will be made available from the lecture notes page. Lecture notes must be taken in the lectures.
Supplementary reading (highly recommended): A good introductory book to financial calculus and the first half of the course is:
- M. Baxter and A. Rennie, Financial Calculus: An Introduction to Derivative Pricing, Cambridge University Press, Cambridge, 1996.
A good introductory book for the second half of the course is:
- F. C. Klebaner, Introduction to Stochastic Calculus with Applications, Imperial College Press, London, 1998.
Advanced level books include:
- B. Oksendal, Stochastic Differential Equations: An Introduction with Applications, 5th edition, Springer-Verlag, New York, 1998.
- H. J. Kushner and P. G. Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time, Springer-Verlag, New York, 1992.
Web: The course web page is at http://www.maths.uq.edu.au/courses/MATH4091. Information about the course and other resources are available there.

Assessment

Assessment Scheme: There will be four (4) assignments each counting ten (10) percent of the assessment and a final two (2) hour examination counting sixty (60) percent of the assessment.
Submission of assignments: Assignments must be submitted in your tutorial session. Late assignments attract a 1 mark penalty for every day it is overdue.
Dates for submission are
Assignment 1: 17th March
Assignment 2: 7th April
Assignment 3: 12th May
Assignment 4: 2nd June
Marks are awarded for correctness and clarity of presentation. One bonus mark per assignment may be awarded for innovative solutions. Part marks will be awarded for the successful completion of subtasks. Some sample marking schemes will be distributed during the semester.
If you miss an assignment: In case of illness (or bereavement) you may be exempted from an assignment if a medical certificate (or other documentation) is received by the course co-ordinator within one week of the due date of the assignment. If you are exempted, then your assignment marks are weighted on a pro-rata basis. Note that ad hoc excuses (car trouble and the like!) will not be accepted; only documentation in connection with illness or bereavement . If you enrolled late then exemption will automatically be granted for anything missed before the date of enrolment.
Final Examination: The final exam is closed book 2 hours long which will be held in the examinations period at a time and place to be advised by examinations section. Calculators without ASCII capabilities are permitted.
Anything discussed in lectures is examinable. In addition problems from assignments and tutorials as well as similar problems may form part of the written exam.
If you miss the final exam: See the Official Examination Policies at the Resources Page http://www.maths.uq.edu.au/courses/MATH4091/Resources.html This page contains a lot of useful information about examinations as well as about available resources.
Failure to complete assessment items: Failure to complete any item of assessment will result in a weighting of zero for that item except as provided for under the heading "If you miss the final exam".
For information on Plagiarism, Help available for students with disabilities, University policy on Special and Supplementary Examinations, Feedback on Assessment, Assistance for students, or The student Liason Officer, visit http://spider.sps.uq.edu.au/course_profile_info.pdf
Assessment Criteria:
- To earn a Grade of 7, a st udent must demonstrate an excellent understanding of all of the theory. This includes clear expression of nearly all their deductions and explanations, the use of appropriate and efficient mathematical techniques and accurate answers to nearly all questions and tasks with appropriate justification.
- To earn a Grade of 6, a student must demonstrate a comprehensive understanding of the theory of advanced analysis. This includes clear expression of most of their deductions and explanations, the general use of appropriate and efficient mathematical techniques and accurate answers to most questions and tasks with appropriate justification.
- To earn a Grade of 5, a student must demonstrate an adequate understanding of the course theory. This includes clear expression of some of their deductions and explanations, the use of appropriate and efficient mathematical techniques in some situations and accurate answers to some questions and tasks with appropriate justification.
- To earn a Grade of 4, a student must demonstrate an understanding of the basic concepts of advanced analysi s. This includes occasionally expressing their deductions and explanations clearly, the occasional use of appropriate and efficient mathematical techniques and accurate answers to a few questions and tasks with appropriate just ification. They will have demonstrated knowledge of techniques used to solve problems and applied this knowledge in some cases.
- To earn a Grade of 3, a student must demonstrate some knowledge of the basic concepts of advanced analysis. This includes occasional expression of their deductions and explanations, the use of a few appropriate and efficient mathematical techniques and attempts to answer a few questions and tasks accurately and with appropriate justification. They will have demonstrated knowledge of techniques used to solve problems.
- To earn a Grade of 2, a student must demonstrate some knowledge of the basic concepts of advanced analysis. This includes attempts at expressing their deductions and explanations and attempts to answer a few questions accurately.
- A student will receive a Grade of 1 if they demonstrate extremely poor knowledge of the basic concepts in the course material. This includes attempts at answering some questions but showing an extremely poor understanding of the key concepts.

MATH4091 Web Page.