# BSc International Business, Finance and Economics with Industrial/Professional Experience

Year of entry: 2020

## 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. In view of the specific character of the course, lecture podcasts are typically not available for students, and attendance at lectures is therefore particularly important. However, students registered with the DAS Service may, via their Support Plan, request that podcasts be made available to them.

### Pre/co-requisites

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

### 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. 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

The following topics are covered:

•       The Markowitz mean-variance portfolio theory.

•       Capital Asset Pricing Model (CAPM).

•       Factor models: 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.

•       Evolutionary models of financial markets.

### Teaching and learning methods

Lectures, exercise classes and tutorial classes.

### Employability skills

Analytical skills
Synthesis and analysis of data and information. Critical reflection and evaluation.
Problem solving
Research
Planning independent research using library, electronic and online resources.
Other
Presentation. Numeracy. Literacy. Computer literacy. Time-management. Applying subject knowledge. Improving own learning.

### Assessment methods

80%      Exam

10%      Take home test 1

10%      Take home test 2

### Feedback methods

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.,

•       1997.

•       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 to the web during the semester.

### Study hours

Independent study hours
Independent study 0

### Teaching staff

Staff member Role
Igor Evstigneev Unit coordinator