Please note: there may be some adjustments to the teaching arrangements published in the course catalogue for 2020-21. Given current circumstances related to the Covid-19 pandemic it is anticipated that some usual arrangements for teaching on campus will be modified to ensure the safety and wellbeing of students and staff on campus; further adjustments may also be necessary, or beneficial, during the course of the academic year as national requirements relating to management of the pandemic are revised.

## 5E: Mathematical Finance MATHS5081

• School: School of Mathematics and Statistics
• Credits: 10
• Level: Level 5 (SCQF level 11)
• Typically Offered: Semester 2
• Available to Visiting Students: Yes
• Available to Erasmus Students: Yes

### Short Description

The aim of this course is to provide an overview of the uses of mathematics and statistics in finance. The course will provide details of some probabilistic and statistical methods used in finance. Applications of mathematical, optimisation and probabilistic methods from other courses will be described. An introduction to the ideas of derivative pricing, portfolio management will be provided.

### Timetable

17 x 1 hr lectures and 6 x 1 hr tutorials in a semester

### Requirements of Entry

The normal requirement is that students should have been admitted to an Honours- or Master's-level programme in Mathematics and/or Statistics

### Excluded Courses

4H: Mathematical Finance

### Assessment

End-of-Course Examination 90%

Coursework 10%

Main Assessment In: April/May

### Course Aims

To provide an overview of the uses of mathematics and statistics in finance;

To provide details of some probabilistic and statistical methods used in finance;

To describe applications of mathematical, optimisation and probabilistic methods from other courses;

To provide an introduction to the ideas of derivative pricing, portfolio management.

### Intended Learning Outcomes of Course

By the end of this course students will be able:

to explain the idea of time value of money, interest rates, and the arithmetic of compounding and discounting; and to implement these concepts by performing concrete computations;

to describe basic financial products (bonds, stocks) and explain and apply the idea and terminology of futures contracts (long, short positions, hedging, arbitrage);

to explain basic concepts and principles of mathematical finance in the context of one-period models (arbitrage, risk-neutral measures), and to apply these concepts in finite market models and perform example computations;

to describe the basic terminology for options (call, put, American, European) as well as be able to create graphs and explain their payouts;

to explain how options can be implemented in one-period market models, how inequalities for their prices can be derived and the concept of market completeness; to apply these concepts;

to explain and apply the basic concepts of mathematical finance in the context of multiperiod models (price- and value processes, arbitrage, martingale measures), to describe their manifestation in the particular case of the CRR (or binomial) model, and to carry out calculations for pricing options in this model;

to derive the Black-Scholes model by considering limits of discrete time models, and to use it to price contingent claims

to describe the properties of the Black-Scholes model using geometric Brownian motions and Ito's formula

to explain and apply different approaches to measure and manage risk (e.g. the Greeks, Value-at-Risk, the mean-variance approach.

to describe and apply more exotic derivatives (options depending on the average or maximum of the stock price)

to explain and apply the basic ideas of mathematical finance in continuous time (Wiener process, Geometric Brownian motion, Ito's formula)

### Minimum Requirement for Award of Credits

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.