#### Course overview

This module provides an introduction to the most important mathematical concepts and tools used in financial modelling and engineering. The understanding of these tools will be reinforced through introduction to numerical and computational methods and techniques for the practical implementation of these.

The focus will mainly be on the pricing of so-called derivatives, an important task in financial engineering and risk analysis. The field of derivative pricing is a sufficiently rich and mathematically challenging that it calls for a wide range of mathematical tools. These tools are, however, also useful in many other areas of finance.

Many of the models and results found in the mathematical analysis of derivative pricing cannot be solved for analytically. The students are therefore also taught how to implement these using numerical methods.

Students will learn how to implement these numerical methods in the mathematical programming language Matlab.

#### Learning outcomes

- Understand the mathematical concepts and tools underlying modern asset pricing models
- Manipulate and apply these tools to solve a range of finance and investment problems.
- Understand how to implement these mathematical tools in practice using numerical methods
- Learn how to use the mathematical programming languages Matlab for the practical implementation of numerical methods

#### Topics covered

- Numerical Integration and Differentiation
- Ordinary Differential Equations (ODE’s); Numerical Solutions to ODE’s
- Stochastic Processes; Stochastic Differential Equations (SDE’s)
- Numerical Solutions to SDE’s
- Partial Differential Equations (PDE’s); Numerical Solutions to PDE’s
- Monte Carlo (MC) methods
- Programming in Matlab

#### Assessment summary

Unseen Examination (2 hours) 80% Group Coursework 20%

Current students should refer to Moodle for specific details of the current year’s assessment.

#### Essential reading

The following books contains the core material covered in the lectures, neither of which are required reading:

- Rüdiger Seydel, 2012, Tools for Computational Finance, 5th edition, Springer-Verlag.
- Jörg Kienitz and Daniel Wetterau, 2012, Financial Modelling: Theory, Implementation and Practice with Matlab, Wiley.
- Paul Glasserman, 2004, Monte Carlo Methods in Financial Engineering, Springer-Verlag.

#### Past versions of this module

*Last updated Friday, 17 August 2018*