35366 Numerical Methods of Finance
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Credit points: 6 cp
Result type: Grade and marks
Requisite(s): 25839 Mathematics of Finance
These requisites may not apply to students in certain courses. See access conditions.
Description
This subject presents various numerical methods used in quantitative finance. It provides a rigorous understanding of advanced numerical, statistical and filtering methods. Emphasis is on simulation methods for solving stochastic differential equations, their systematic application and their links to finite difference and other numerical methods.
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)
- 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)
- 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 aim of this subject is to present various numerical methods used in modern Quantitative Finance. It deepens the mathematical concepts, numerical techniques and intuition necessary for modern financial modelling, derivative pricing, portfolio optimization and risk management. This subject provides a rigorous understanding of advanced numerical and statistical methods in finance.
Content (topics)
• Stochastic Expansions
• Scenario Simulation
• Estimation of Discretely Observed Diffusions
• Filtering in Finance
• Monte Carlo Simulation
• Numerical Stability
• Variance Reduction Techniques
• Trees and Markov Chains.
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. |
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| 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, 1.1, 3.1 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 and 1.1 |
| 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
Students must achieve at least 50% of the subject’s total marks.
Other resources
1. Reading Material
The course will be based on the book "Numerical Solution of SDEs with Jumps in Finance" by Eckhard Platen and Nicola Bruti-Liberati and the book "A Benchmark Approach to Quantitative Finance" by Eckhard Platen and David Heath.
2. Lecture Slides
The presented lecture slides will be provided electronically as course material.
3. Exercises
Exercises are included in the lecture notes at the end of each chapter.
4. References
- Platen, E. and Bruti-Liberati, N. (2010) Numerical Solution of Stochastic Differential Equations with Jumps in Finance, Springer. / Kloeden, P.E. and Platen, E. (1999) Numerical Solution of Stochastic Differential Equations, Vol 23 of Applied Math., Springer, Third corrected printing.
- Kloeden, P.E; Platen, E. and Schurz, H. (2003} Numerical Solution of SDE's Through Computer Experiments, Universitext, Springer, Third corrected printing.
- Platen, E. and Heath, D. (2010) A Benchmark Approach to Quantitative Finance, Springer Finance.
- Seydel, R. (2002) Tools for Computative Finance, Universitext, Springer.
- Wilmott, P.; Dewynne, J. and Howison, S. (1996) Option Pricing: Mathematical Models and Computation, Oxford Financial Press.