37003 Application of Numerical and Computational Approaches A
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Credit points: 8 cp
Subject level:
Postgraduate
Result type: Grade and marksRequisite(s): 24 credit points of completed study in spk(s): STM91543 Core Subjects (Mathematics) OR 24 credit points of completed study in spk(s): STM91515 Core Subjects (M Quantitative Finance)
These requisites may not apply to students in certain courses. See access conditions.
Anti-requisite(s): 25871 Computational Methods and Model Implementation
Description
Given the increasing complexity of financial markets, numerical and computational methods for solving quantitative finance problems have become essential to derive concrete insights from sophisticated financial models. This subject is the first of two capstone subjects which concentrate on developing practical skills for solving quantitative finance problems using numerical and computational techniques. In this subject, students will conceptualise and articulate a quantitative finance problem based on current industry examples and emerging industry trends and devise and execute a suitable theoretical and computational framework for solving the problem.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
| 1. | Identify and articulate a quantitative finance problem, including its context, motivation, and implications on academic literature and/or quantitative finance practice |
|---|---|
| 2. | Formulate a sound framework to solve a chosen quantitative finance problem |
| 3. | Identify, understand, and apply mathematical, statistical, and quantitative techniques required to address and solve the chosen quantitative finance problem |
| 4. | Implement the designed computational/numerical framework in Python |
| 5. | Report, in both written and oral forms, the chosen quantitative finance problem and the proposed methodological framework using professional language |
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)
- Investigate complex and challenging real-world problems in the areas of quantitative finance by critically evaluating information and solutions and conducting appropriate approaches to independent research. (2.1)
- 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)
- Reflect and evaluate the value, integrity, and relevance of multiple sources of information to derive responsive, innovative solutions, show creativity, innovation and application of technologies in complex quantitative finance problems. (4.1)
- Develop and present complex ideas and justifications using appropriate communication approaches from a variety of methods (oral, written, visual) to communicate with mathematicians, data analysts, scientists, industry, and the general public. (5.1)
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:
GA 1. Disciplinary Knowledge – acquire detailed specialised quantitative finance knowledge and professional competency required to work as a quantitative finance analyst in the modern finance industry
GA 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.
GA 3. Professional, Ethical, and Social Responsibility – develop an enhanced capacity to work ethically and professionally in the workplace
GA 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.
GA 5. Communication – develop professional communication skills for a range of technical and non-technical audiences.
Teaching and learning strategies
This subject is a directed and independent study subject culminating in a capstone project output. Students are guided by the teaching staff in the identification and articulation of a quantitative finance problem and in the identification of relevant mathematical, statistical, and quantitative techniques that may be involved in resolving the quantitative finance problem. Students are given access to a catalogue of learning materials on relevant computational and numerical approaches, but students are responsible for learning and understanding the methods that are relevant to their chosen quantitative finance problem. Such design mirrors the type of task a quantitative finance professional may expect to face: implementing a new model or method, calibrating a model to market data, pricing financial derivatives, measuring and managing risks, and performing other calculations required to solve problems arising in practice.
Students are required to submit written reports documenting their progress throughout the subject and will be provided written and oral feedback by the teaching staff. Students are also required to engage explicitly with their peers’ work through oral presentations where they are required to field questions from the audience.
Content (topics)
In the context of their chosen quantitative finance problem, students shall employ a subset of the following numerical and computational approaches:
- Optimization (in the context of quantitative finance)
- Model calibration with examples in interest rate term structure models and volatility models
- Adjoint differentiation and neural networks (with illustrations in formulating hedging strategies)
- Monte Carlo methods (including variance reduction techniques)
- Numerical solution of stochastic differential equations
- Numerical solution of partial differential equations
Assessment
Assessment task 1: Motivation and Statement of the Problem
| Intent: | This assessment task contributes to the development of the following graduate attributes: |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1 and 3 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 2.1, 3.1, 4.1 and 5.1 |
| Type: | Project |
| Groupwork: | Individual |
| Weight: | 40% |
| Criteria: | Students will be assessed primarily on the content (the level of understanding of the chosen quantitative finance problem and the required numerical/computational approaches) [CILO 1.1, CILO 2.1], a reflection on the data requirements to resolve the problem [CILO 3.1], the level of reflection on the problem’s relevance to academic literature and/or industry practice [CILO 4.1], and the clarity and organization of the written report [CILO 5.1]. |
Assessment task 2: Framework and Methodology
| 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, 3, 4 and 5 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 2.1, 3.1, 4.1 and 5.1 |
| Type: | Project |
| Groupwork: | Individual |
| Weight: | 40% |
| Criteria: | Students will be assessed primarily on the content (the level of understanding of the mathematical concepts/theory and the numerical/computational approaches required to solve the problem) [CILO 1.1, CILO 2.1], the level of reflection on and of the articulation of the data requirements to resolve the problem [CILO 3.1], the level of reflection on the relevant/related literature and how it informs the proposed conceptual/theoretical framework and proposed methodology [CILO 4.1], and the clarity and organization of the written report [CILO 5.1]. |
Assessment task 3: Oral Presentation
| 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 5 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 2.1, 3.1 and 5.1 |
| Type: | Project |
| Groupwork: | Individual |
| Weight: | 20% |
| Criteria: | Students will be assessed on their understanding of the chosen quantitative finance problem and the numerical/computational methods they propose to address the problem [CILO 1.1, CILO 2.1], on their engagement with their peers in a professional and respectful manner [CILO 3.1], and on the clarity and organisation of their oral presentation and the manner in which they address audience questions [CILO 5.1]. |
Minimum requirements
Students must achieve at least 50% of the subject’s total marks to pass the subject.
Required texts
There is no textbook.
Recommended texts
The following references are useful for understanding how to use Python in for computational tasks:
Hans Petter Langtangen (2012). A Primer on Scientific Programming with Python, 3rd edition, Springer.
Irv Kalb (2016). Learn to Program with Python, Apress.
Joey Bernard (2016). Python Recipes Handbook: A Problem-Solution Approach, Apress.
PDF versions of these books can be downloaded for free from the UTS library.
The teaching staff shall provide recommended references related to specific computational and/or numerical methods upon request.