Year of entry: 2018
Course unit details:
|Unit level||Level 3|
|Teaching period(s)||Semester 2|
|Available as a free choice unit?||Yes|
See course Blackboard pages.
|Unit title||Unit code||Requirement type||Description|
|Mathematical Economics I||ECON20120||Pre-Requisite||Compulsory|
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.
The following topics will be covered:
- The Markowitz mean-variance portfolio theory.
- Capital Asset Pricing Model (CAPM).
- Factor models: the Ross-Huberman arbitrage pricing theory (APT).
- One-period and multiperiod discrete-time models of securities markets.
- Hedging strategies and pricing by no-arbitrage.
- Fundamental Theorem of Asset Pricing.
- Pricing European and American options in binomial models.
- The Black-Scholes formula (via binomial approximation).
Growth-optimal investments and the Kelly portfolio rule.
Teaching and learning methods
Lectures, exercise classes and tutorial classes.
- Analytical skills
- Synthesis and analysis of data and information. Critical reflection and evaluation.
- Problem solving
- Planning independent research using library, electronic and online resources.
- Presentation. Numeracy. Literacy. Computer literacy. Time-management. Applying subject knowledge. Improving own learning.
- Weighting: 80%.
- Date: May/June examination period.
- Length: 1.5 hours.
- Structure: 3/5 questions, all questions carry equal weight.
Two Take-Home Tests:
- Weighting: 20%.
Students can get feedback and additional support at small-group tutorial meetings and weekly office hours.
- I. Evstigneev, T. Hens and K.R. Schenk-Hoppé, Mathematical Financial Economics, Springer, 2015.
- H. H. Panjer (Editor), Financial Economics, The Actuarial Foundation of the USA, 1998.
- D. Luenberger, Investment Science, Oxford University Press, 1998.
- S. Ross, An introduction to Mathematical Finance, Cambridge University Press, 1999.
- S. R. Pliska, Introduction to Mathematical Finance: Discrete Time Models, Blackwell Publ.,
- H. Föllmer 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 on the web during the semester.
|Scheduled activity hours|
|Practical classes & workshops||2|
|Independent study hours|
|Igor Evstigneev||Unit coordinator|