37005 Fundamentals of Derivative Security Pricing
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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)
These requisites may not apply to students in certain courses. See access conditions.
Anti-requisite(s): 25873 Fundamentals of Derivative Security Pricing
Description
This subject introduces the basic concepts for the pricing of derivative securities from an intuitive perspective. Topics include; arbitrage pricing in continuous time, different interpretations of the arbitrage pricing condition, leading to the partial differential equation, martingale and integral evaluation viewpoints. Exotic options, American option and option pricing under stochastic volatility are also considered.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
| 1. | Understand the assumptions and the mathematical background of derivative pricing theory in continuous time. |
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| 2. | Implement the theoretical models of continuous time finance and to develop intuition for the underlying financial issues and aspects such as arbitrage-free derivative pricing, martingales, stochastic volatility and jump-diffusion models. |
| 3. | Understand available literature on derivative securities pricing. |
| 4. | Price derivative securities from both the partial differential equation and the martingale viewpoints. |
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)
- 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 the various financial and mathematical concepts, techniques and intuition necessary to price derivative securities in a non-stochastic interest rate environment. This subject introduces students to the modelling of asset price dynamics in continuous time, the arbitrage pricing of derivatives in continuous time, interpretations of the arbitrage pricing condition leading to the partial differential equation, martingale and integral evaluation viewpoints. American options and option pricing under stochastic volatility and jump-diffusion dynamics will also be introduced. The focus of the subject is on the development of economic intuition behind the various concepts. Implementation of some models on the computer will also form part of the subject requirements.
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.
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.
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.
5. Communication - Effective professional communication skills for a range of technical and non-technical audiences.
Teaching and learning strategies
This subject will use the ‘blended learning’ model where students will have access to online learning resources and will undertake learning tasks prior to coming to in-person tutorials. Essential principles are presented and analysed in the online lecture component and this is complemented by students going through practical application exercises under the guidance of the lecturer in the tutorials. In this way, the subject will enable students to experience an effective integration of online and face-to-face on-campus learning.
Lecture Program
Outlined schedule indicates topics to be discussed in lectures. The recommended theory and computational problems constitute the set that should be attempted - this includes additional recommended problems which will be announced as you progress through the subject. Students should complete all the recommended problems
The aim of the lectures is to provide an overview of the main concepts and techniques covered in the indicated chapters in the textbook, as well as material supplementing the textbook. The lectures should be seen as a useful guide to reading the textbook and doing the recommended problems. It is essential that you also read the recommended chapters in the textbook and do the recommended theory and computational problems.
Studying Derivatives
This subject is a challenging subject to study due to the demanding technical level of the material. It is recommended that you have read the required chapters before you view the relevant online lecture. This will assist in clarifying issues related to the assigned topics covered in the lecture and will increase your understanding.
Computer Exercises
You will need access to a computer (running MS Windows, Linux or macOS), since programming in Python is an important part of this subject. In keeping with authentic assessment, some of these exercises will be conducted on real-world financial data. In order to provide early feedback, these exercises will be assigned in several parts over the teaching period and feedback will be provided on each completed part before the next part is due.
Tutorials
Online recorded lectures in this subject will be complemented by in-person tutorials. In these tutorials, you will work in small groups to collaboratively solve mathematical problems in derivative security pricing on a whiteboard ("whiteboard tutorials"). The lecturer will provide formative feedback to each group as they develop their solutions during the tutorials. Before each tutorial, you should make sure that you have watched all recorded lectures and read all relevant textbook chapters of the previous weeks.
Content (topics)
- Basic option pricing problem, concepts, and techniques in single-period model
- Black-Scholes option pricing: hedging, risk-neutral valuation, martingale and PDE approaches
- A general approach including numeraire approach to pricing multi-factor derivative securities and applications to exchange and/or currency options
- The martingale interpretation of the derivative pricing equation, market prices of risk of driving factors, change of measure, and risk neutral valuation
- Option pricing under stochastic volatility dynamics and volatility smiles
- Exotic options and American options.
Assessment
Assessment task 1: Assignment (Group)
| 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 and Creativity. 5. Communication. |
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| 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, 1.1 and 5.1 |
| Groupwork: | Group, group assessed |
| Weight: | 20% |
| Criteria: | Disciplinary knowledge is demonstrated by the correctness of the derivative pricing and risk management solution. Reflection, innovation and creativity is demonstrated by the implementation of the solution on real-world data, i.e. by way of authentic assessment. Research, enquiry and critical thinking is assessed by requiring students to demonstrate an understanding of the practical implications of the mathematical and numerical results, which must be effectively communicated in the assignment report. |
Assessment task 2: Assignment (Individual)
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary Knowledge 4. Reflection, Innovation, Creativity. 5. Communication. |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2 and 4 This assessment task contributes to the development of course intended learning outcome(s): .1, 1.1 and 5.1 |
| Groupwork: | Individual |
| Weight: | 30% |
| Criteria: | Disciplinary knowledge is demonstrated by the correctness of the derivative pricing and risk management solution. Reflection, innovation and creativity is demonstrated by the implementation of the solution on real-world data, i.e. by way of authentic assessment. Reflection is further demonstrated by qualitatively interpreting quantitative results, which must be effectively communicated in the assignment report. |
Assessment task 3: Written and Oral Exam (Individual)
| Intent: | The final examination will test students' knowledge and competencies in applying financial techniques to solve problems. This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary Knowledge 4. Reflection, Innovation, Creativity. |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 3 and 4 This assessment task contributes to the development of course intended learning outcome(s): .1 and 1.1 |
| Groupwork: | Individual |
| Weight: | 50% |
| Length: | 2 hours and 10 minutes, including 10 minutes reading time. |
| Criteria: | Disciplinary knowledge is demonstrated by the correctness of the derivative pricing and risk management solution. Furthermore, applying the disciplinary knowledge in the context of a new problem in this assessment task will demonstrate reflection, innovation and creativity. |
Minimum requirements
Students must achieve at least 50% of the subject’s total marks.
Required texts
Chiarella, C., X. He and C. Sklibosis Nikitopoulos, 2015, Derivative Security Pricing: Techniques, Methods and Applications, Springer.
References
Bjork, T. 2004, Arbitrage Theory in Continuous Time, 2nd edn., Oxford University Press.
Mikosch, T. 1998, Elementary Stochastic Calculus with Finance in View. World Scientific.
Neftci, S.N. 2000, An Introduction to the Mathematics of Financial Derivatives, 2nd edn., Academic Press.
Schlögl, E. 2014, Quantitative Finance: An Object-Oriented Approach in C++, Chapman & Hall
Shreve, S. 2004, Stochastic Calculus for Finance I: The Binomial Asset Pricing Model, Springer
Shreve, S. 2004, Stochastic Calculus for Finance II: Continuous Time Models, Springer