# BA Modern Language and Business & Management (French) / Course details

Year of entry: 2022

## Course unit details:Mathematical Finance

Unit code ECON30382 10 Level 3 Semester 2 Economics Yes

### Overview

Mathematical Finance is an area at the interface of Mathematical Economics and Finance concerned with the mathematical modelling of financial markets. 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---primarily markets for derivative securities---based on concepts and theory developed by academics. Nowadays, the turnovers of these markets are measured in billions. This is perhaps the only example in the history of Economics when principles that have led to the emergence of a new economic reality were discovered by mathematicians “on the tip of the pen”.

Standard courses on Mathematical Finance rely upon advanced mathematical techniques, first of all, stochastic calculus. This course is one of very few exceptions. It introduces students to the whole wealth of ideas of Mathematical Finance using only elementary mathematics understandable for 3rd year economics students. The course served as one of the main sources for the textbook by I.V. Evstigneev, T. Hens and K.R. Schenk-Hoppé “Mathematical Financial Economics: A Basic Introduction” (Springer, 2015), which is suggested as the main reading for students.

The syllabus covers classical topics, such as mean-variance portfolio analysis and no-arbitrage theory of derivative securities pricing. A less standard but very important topic, which is typically not covered in introductory courses on Mathematical Finance, is capital growth theory (Kelly, Cover and others). Absolutely new material, reflecting research achievements of recent years, is an introduction to new dynamic equilibrium models of financial markets combining behavioural and evolutionary principles.

Although this course assumes the knowledge of only elementary mathematical techniques suitable for undergraduate economics students, it involves rigorous reasoning---theorems, assumptions, proofs, etc., and is addressed to students inclined to mathematics.

### Pre/co-requisites

Unit title Unit code Requirement type Description
Mathematical Economics I ECON20120 Pre-Requisite Compulsory
Pre-requisites: ECON20120

ECON20120 Math Econ

### Aims

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.

### Learning outcomes

By the end of this course you will be able to:

1. Understand and apply the basic theory, tools, and terminology of Mathematical Finance.
2. Formalise real world situations by using models and techniques suggested by the theory.
3. Solve numerically typical problems related to asset pricing and risk management.

### Syllabus

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

### Employability skills

Other
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.

### Assessment methods

90%      Exam

5%      Take home test 1

5%      Take home test 2

### Feedback methods

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.

### Teaching staff

Staff member Role
Igor Evstigneev Unit coordinator