37007 Probability Theory and Stochastic Analysis
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Subject handbook information prior to 2025 is available in the Archives.
Credit points: 8 cp
Result type: Grade and marks
Requisite(s): 68105 Algebra AND 68106 Calculus 1 AND 37161 Probability and Random Variables
These requisites may not apply to students in certain courses.
There are course requisites for this subject. See access conditions.
Anti-requisite(s): 25875 Probability Theory and Stochastic Analysis
Description
Stochastic modelling in financial applications relies on advanced techniques from probability theory and stochastic analysis that are used extensively for derivative pricing and hedging, interest rate modelling and risk management. This subject introduces students to many fundamental concepts and results required in financial applications. Due to diversity in students’ skills, students start from basic concepts and gradually move to advanced methodologies. This subject is illustrated with applications in R (and other languages) of modelling and simulation of random dynamics. Responding to an increasing need from industry, students demonstrate these techniques by solving a number of programming exercises in the assignment assessment task.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
| 1. | Model evolution of random phenomena using standard tools from stochastic analysis. |
|---|---|
| 2. | Apply stochastic processes in finance and risk management. |
| 3. | Implement and analyse complex dynamical models using techniques from stochastic analysis |
Course intended learning outcomes (CILOs)
This subject also contributes specifically to the development of following course intended learning outcomes:
- Appraise advanced knowledge and critically evaluate the information's source and relevance, with a focus on applications of mathematical methodologies to quantitative finance problem solving. (1.1)
- Practice professionally adhering to confidentiality requirements, ethical conduct, data management, and organisation and collaborative skills in the context of applying mathematical and statistical modelling to quantitative finance problems. (3.1)
Contribution to the development of graduate attributes
The Faculty of Science has determined that our courses will aim to develop the following attributes in students at the completion of their course of study. Each subject will contribute to the development of these attributes in ways appropriate to the subject, thus not all attributes are expected to be addressed in all subjects.
This subject contributes to the development of the following graduate attributes:
1. Disciplinary Knowledge - acquire detailed specialised quantitative finance knowledge and the professional competency required to work as a quantitative finance analyst in the modern finance industry.
2. Research, inquiry and critical thinking - develop the ability to apply and demonstrate critical and analytical skills to developing solution to complex real world problems.
3. Professional, Ethical and Social Responsibility - develop an enhanced capacity to work ethically and professionally using collaborative skills in the workplace.
4. Reflection, Innovation and Creativity – develop the ability source and analyse multiple sources of data to develop innovative solutions to real world problems in quantitative finance.
Teaching and learning strategies
This subject is taught with a three hour weekly seminar, each combining a lecture and tutorial/lab component. In these classes, students will learn, practise and ask questions and discuss the application of probability and stochastic analysis to the field of mathematical finance.
The lecture component of the seminars comprise theory and supporting examples where the principles of probability and stochastic analysis are introduced and explored. The tutorial/lab components show how these ideas can be applied in practical settings, using R and other programming languages as computational aids.
Because the subject content builds cumulatively, as preparation for each week's class students must have learnt the material from the preceding week. The material in each week’s tutorial/lab component will be based on the content of that week’s lecture component, illustrating the necessity for students to progressively learn the theoretical material as the semester proceeds.
Before the first week of class, students are expected to familiarise themselves with Canvas. The subject outline, theoretical material, tutorial/lab problems, assignment questions and other material will be made available through Canvas.
In Week 1 the lecturer will provide details of consultation times, during which students may request assistance that could not be provided during formal class sessions. Questions may also be asked via email (address listed at top of document), with responses to be provided within two working days.
Content (topics)
Conditional expectation, mulltivariate normal distribution. Theorem on normal correlation.
Gaussian, stationarity, and Markov processes. Statte space modelling.
Martingales, change-of-numeraire transformation.
Stochastic calculus, stochastic differential equations. Feynman-Kac formula with applications.
Assessment
Assessment task 1: Take-home assignment
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary knowledge. |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2 and 3 This assessment task contributes to the development of course intended learning outcome(s): .1, .1, 1.1 and 3.1 |
| Type: | Exercises |
| Groupwork: | Individual |
| Weight: | 50% |
| Criteria: | Marks to be awarded based on:
|
Assessment task 2: Final exam
| Intent: | This assessment task contributes to the development of the following graduate attributes: |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2 and 3 This assessment task contributes to the development of course intended learning outcome(s): .1, .1 and 1.1 |
| Type: | Examination |
| Groupwork: | Individual |
| Weight: | 50% |
| Criteria: | Marks to be awarded based on:
|
Minimum requirements
Students must achieve at least 50% of the subject’s total marks. The final exam is an open book exam.