Year of entry: 2022
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Course unit details:
|Unit level||Level 3|
|Teaching period(s)||Semester 2|
|Available as a free choice unit?||Yes|
|Unit title||Unit code||Requirement type||Description|
|Mathematical Economics I||ECON20120||Pre-Requisite||Compulsory|
ECON20120 Math Econ
The purpose of the course is to present fundamental ideas and tools developed at the interface of Mathematical Economics and Finance. A central goal is to demonstrate the use of these tools in contexts where they are indispensable and widely exploited. A remarkable feature of Mathematical Finance is that its theoretical highlights (such as the Black-Scholes formula) turned out to be extremely important in practice. They have created new markets essentially based on concepts developed by academics. The course will expose students to quantitative techniques and theory that will be useful to any actor in the financial industry: a portfolio manager, a risk management consultant, or a financial analyst.
By the end of this course you will be able to:
- Understand and apply the basic theory, tools, and terminology of Mathematical Finance.
- Formalise real world situations by using models and techniques suggested by the theory.
- Solve numerically typical problems related to asset pricing and risk management.
Topics will include the following:
1. The Markowitz mean-variance portfolio theory.
2. Capital Asset Pricing Model (CAPM).
3. Factor models: Ross-Huberman arbitrage pricing theory (APT).
4. One-period and multiperiod discrete-time models of securities markets.
5. Hedging strategies and pricing by no-arbitrage.
6. Fundamental Theorem of Asset Pricing.
7. Pricing European and American options in binomial models.
8. The Black-Scholes formula (via binomial approximation).
9. Growth-optimal investments and the Kelly rule.
Teaching and learning methods
Synchronous activities (such as Lectures or Review and Q&A sessions, and tutorials), and guided self-study
- The demand for highly skilled experts in finance and financial economics continues to increase rapidly in the modern economy. This demand exists in the public sector (e.g. central banks and international organisations) and especially in the private sector (e.g. commercial banks and investment companies). This course is designed for those students who wish to pursue a future career in the realms of financial economics and finance. It combines an introduction to fundamental principles of investment science and training in the mathematical methods needed for the analysis of financial markets.
5% Take home test 1
5% Take home test 2
Students can get feedback and additional support at small-group tutorial meetings and weekly office hours.
1. I. Evstigneev, T. Hens and K.R. Schenk-Hoppé, Mathematical Financial Economics, Springer, 2015.
2. H. H. Panjer (Editor), Financial Economics, The Actuarial Foundation of the USA, 1998.
3. D. Luenberger, Investment Science, Oxford University Press, 1998.
4. S. Ross, An introduction to Mathematical Finance, Cambridge University Press, 1999.
5. S. R. Pliska, Introduction to Mathematical Finance: Discrete Time Models, Blackwell Publ., 1997.
6. H. Follmer and A. Schied, Stochastic Finance: An Introduction in Discrete Time, Walter de Gruyter, 2002.
This reading is supplementary to the lectures and is optional. The course is self-contained, and no external texts or resources are required to fulfill its objectives. Electronic pdf copies of all course materials (lecture notes/slides, exercises and answers) will be posted to the web during the semester.
Those who wish to study the subject more deeply are referred to the textbook . This is the only text in the literature that combines mathematical rigour with the use of only elementary mathematical techniques suitable for Economics students. Other books in the above list require knowledge of advanced mathematics.
|Igor Evstigneev||Unit coordinator|
For every 10 course unit credits we expect students to work for around 100 hours. This time generally includes any contact times (online or face to face, recorded and live), but also independent study, work for coursework, and group work. This amount is only a guidance and individual study time will vary