37006 Application of Numerical and Computational Approaches B
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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 (37003c Application of Numerical and Computational Approaches A AND 24 credit points of completed study in 24.0000000000 Credit Points spk(s): STM91515 Core Subjects (M Quantitative Finance))
The lower case 'c' after the subject code indicates that the subject is a corequisite. See definitions for details.
These requisites may not apply to students in certain courses. See access conditions.
Anti-requisite(s): 25874 Numerical Methods in Finance
Description
Given the increasing complexity of financial markets, the corresponding mathematical models for analysing asset prices and market variables have also grown intricate. Closed-form solutions for problems in quantitative finance, such as derivatives pricing, hedging, portfolio optimisation, equity analysis, yield curve analysis, and risk management, are typically absent under complex models. Therefore, numerical and computational methods have become essential for deriving concrete insights from these intricate financial models.
This subject is one of two capstone subjects that concentrate on developing practical skills for solving quantitative finance problems using numerical and computational techniques. This subject enables students to conceptualise and articulate a quantitative finance problem based on current industry examples, devise and execute a suitable theoretical and computational framework for solving the problem and generate a specialised report communicating their analysis and findings to a target audience.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
| 1. | Define and illustrate the terms used in Numerical Analysis in Finance |
|---|---|
| 2. | Demonstrate and apply discrete time approximation techniques for stochastic differential equations |
| 3. | Simulate the solution of problems involving stochastic differential equations, jump diffusions and solve numerically partial differential equations |
| 4. | Describe modern statistical and filtering methods with applications in finance |
| 5. | Clearly communicate knowledge of the subject matter in numerical and financial contexts and the solutions to problems requiring such knowledge. |
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
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. Disciplinary knowledge is developed in this subject by equipping students with a variety of numerical methods used in the field of quantitative finance including simulation methods, finite difference methods, solutions of stochastic differential equations and filtering methods. Students will gain an in-depth knowledge of mathematical matters and practical issues in numerical problems.
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. Numerical methods used in the field of quantitative finance will be applied to the pricing of derivatives and other problems arising in quantitative finance. In doing so, students will apply critical thinking and inquiry to implement these methods in an innovative manner to solve complex real-world problems.
GA 3 - Professional, ethical and social responsibility – develop an enhanced capacity to work ethically and professionally
using collaborative skills 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. Students will make short presentations in class describing their approach to solving pricing and valuation problems using the methods covered in class. At this point, other students will have the opportunity to comment and make suggestions on how to improve the implementation. This will allow students to work collaboratively on problems and develop innovation and creativity is solving problems. Students will also submit written solutions with detailed explanations of their assumptions, methods and results.
Teaching and learning strategies
The subject is presented in seminar format. Numerical techniques are presented and analysed during the lecture, after which the students are guided through worked examples that illustrate various implementation issues. They are then required to implement the techniques themselves in an assigned programming language, in order to solve prescribed homework problems. Programming is a significant component of the subject.
The teaching and learning strategies in this subject enable students to experience a seamless integration of online and face-to-face learning. Students will have access to online learning resources and will undertake preliminary learning tasks prior to coming to classes where they engage in further learning and practical workshops.
Off campus, students will have access to resources to help introduce theory and concepts before class. These learning resources can be accessed by students at their convenience. In the lectures and workshops, the theory and concepts are further reinforced with real-world examples.
Students will receive feedback during class on their solutions. Students will receive summative feedback on their assignment solutions.
Content (topics)
- Random number generation
- Generating stock price paths
- Monte Carlo methods
- Variance reduction techniques
- Quasi-Monte Carlo methods
- Explicit finite difference schemes
- Implicit difference schemes
- Binomial and trinomial lattices
- Calibrating the volatility surface
Assessment
Assessment task 1: Assignments (Individual)
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1 - Disciplinary Knowledge. 2 - Research, enquiry and critical thinking. 3 - Professional, Ethical and Social Responsibility 4 - Reflection, Innovation, Creativity. 5 - Communication. |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 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 |
| Weight: | 50% |
| Criteria: | Evidence of understanding of the numerical methods techniques presented in lectures and applying these to quantitative finance problems. You will be required to communicate your worked solution through a written report detailing the methods used and discussing the results obtained. |
Assessment task 2: Final Exam (Individual)
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1 - Disciplinary Knowledge. 2 - Research, enquiry and critical thinking. 4 - Reflection, Innovation, Creativity. |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2, 3 and 4 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 2.1 and 4.1 |
| Weight: | 50% |
| Criteria: | The exam questions will involve the application of numerical method techniques presented in lectures to quantitative finance problems. The final exam will assess disciplinary knowledge in terms of the integrity and correctness of the answers and the accuracy of explanations. Innovation, creativity and critical reflection in the answers to questions in the final exam are assessed and recognised. Critical thinking will be integral to successfully solving questions in the final exam. |
Minimum requirements
A pass in the subject is achieved by gaining an overall total of 50% or more of the weighted marks in this subject.
References
Paul Glasserman, Monte Carlo methods in financial engineering, Springer Verlag, 2004, ISBN 0-387-00451-3
Peter Kloeden and Eckhard Platen, Numerical solution of stochastic differential equations, Springer-Verlag, 1992, ISBN 0-387-54062-8
Domingo Tavella and Curt Randall, Pricing financial instruments: the finite difference method, John Wiley & Sons, 2000, ISBN 0-471-19760-2
Paul Wilmott, Sam Howision and Jeff Dewynne, The mathematics of financial derivatives, Cambridge University Press, 1995 ISBN 0-521-49789-2
Other resources
1. Lecture Slides
The presented lecture slides will be provided electronically as course material.
3. Exercises
Exercises will be provide for each lecture.
3. Program Templates
Sample Python code is provided for all of the methods described in this course.