35365 Stochastic Calculus in Finance
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Subject handbook information prior to 2025 is available in the Archives.
Credit points: 6 cp
Result type: Grade and marks
Requisite(s): 35364 Statistics for Quantitative Finance
These requisites may not apply to students in certain courses.
There are course requisites for this subject. See access conditions.
Description
The aim of this subject is to present and deepen the various mathematical concepts, techniques and intuition necessary for modern financial modelling, derivative pricing, portfolio optimisation and risk management. It provides the foundations for a sufficiently rigorous mathematical treatment of these topics. It also enables students to confidently apply the theory of stochastic processes and stochastic calculus.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
| 1. | Define and illustrate the terms used in the study of stochastic processes including Brownian motion, Levy processes, diffusion processes and martingales. |
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| 2. | Demonstrate and apply techniques of stochastic calculus in finance. |
| 3. | Formulate and solve applied and theoretical problems involving stochastic differential equations, diffusions and Lévy processes. |
| 4. | Communicate clearly knowledge of the subject matter in financial contexts and solutions to the problems requiring such knowledge. |
| 5. | Demonstrate preparedness to undertake further study in the mathematics of finance. |
Course intended learning outcomes (CILOs)
This subject also contributes specifically to the development of following course intended learning outcomes:
- Demonstrate critical appraisal of advanced knowledge and critically evaluate the information’s source and relevance, with a focus on applications of mathematical and statistical methodologies to problem solving. (.1)
Contribution to the development of graduate attributes
The material presented in this subject and the method of presentation are linked to the following Science graduate attributes:
- An understanding of the nature, practice and application of the chosen science discipline.
- An understanding of the scientific method of knowledge acquisition, including problem solving, critical thinking, and the ability to discover new understandings.
- The capacity to learn in, and from, new disciplines to enhance the application of scientific knowledge and skills in professional contexts.
- An awareness of the role of science within a global culture.
- An ability to think and work creatively and the ability to apply science skills to unfamiliar applications.
- The ability to develop computing skills.
Teaching and learning strategies
Each week, this subject involves three hours of classes comprised of a lecture and a tutorial. These three hours of classes are supposed to be complemented by regular individual work comprised of studying the material presented in the lectures, solving tutorial problems and working on the assignment.
This subject outline, tutorial questions, and other supporting material will be distributed in class. Some material including the subject outline will be available in UTSOnline.
As a student in this subject you are expected to attend all lectures and tutorials. As preparation for a tutorial, you are expected to attempt all questions distributed prior to this tutorial. As preparation for a lecture, you are expected to learn all material presented in the previous lecture.
If you have further questions or need further help with understanding the subject, please ask the lecturer during the consultation hours. If this is not possible, you can e-mail or phone the lecturer to negotiate a time to meet. Your e-mail messages will be responded to within two working days.
Content (topics)
This subject covers the following topics: theory of Gaussian and Markov processes, diffusions and the Feynman-Kac formula; elements of the theory of martingales and stochastic calculus, stochastic differential equations; change of probability measures; martingale approach to pricing of derivatives and other financial applications.
Assessment
Assessment task 1: Class test
| Objective(s): | This assessment task contributes to the development of course intended learning outcome(s): 1.1 |
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| Weight: | 20% |
Assessment task 2: Assignment
| Objective(s): | This assessment task contributes to the development of course intended learning outcome(s): 1.1 |
|---|---|
| Weight: | 20% |
Assessment task 3: Final examination
| Objective(s): | This assessment task contributes to the development of course intended learning outcome(s): 1.1 |
|---|---|
| Weight: | 60% |
Minimum requirements
Any assessment task worth 40% or more requires the student to gain at least 40% of the mark for that task. If 40% is not reached, an X grade fail may be awarded for the subject, irrespective of an overall mark greater than 50.
Your final mark in this subject will be calculated as follows : Max(E+C+A,E)
where is the mark for the final exam, C is the mark for the class test, is the mark for the assignment.
In order to pass this subject you must get a final mark of at least 50.
References
- Dokuchaev, N. Mathematical Finance. Core Theory, Problems and Statistical Algorithms, Routledge Advanced Texts in Economics and Finance, 2007.
- Borovkov, K. Elements of stochastic modelling. World Scientific Publishing Co., Inc., River Edge, NJ, 2003
- Cont, R. and Tankov, P. Financial Modelling with JumpProcesses. Chapman & Hall, 2004.
- Klebaner, F. Introduction to stochastic calculus with applications. Imperial College Press, London; Second Edition (2006) .(UTS library has Electronic version.)
- Platen, E. and Heath, D. A benchmark approach to quantitative finance. Berlin , Springer, 2006.