# Financial Modelling and Data Science

## Overview

• Credit value: 30 credits at Level 7
• Assessment: coursework (20%) and a three-hour examination (80%)

## Module description

In this module we introduce you to the main mathematical and numerical techniques used in quantitative finance. The module is divided into three parts:

• Stochastic Processes for Finance
• Theoretical Numerical Methods for Finance
• Programming in C++

You will also become acquainted with suitable languages and computer packages for financial applications (C++ and Matlab).

## Learning objectives

By the end of this module, you should:

a) Stochastic Processes for Finance

• understand the basic concepts of stochastic calculus, in particular Brownian motion and stochastic integrals
• understand Ito calculus and its applications to stochastic differential equations (SDEs)
• understand the numerical solution of an SDE
• be able to appreciate the connections between probability theory and partial differential equations via the Feynman-Kac formula

b) Theoretical Numerical Methods for Finance

• be able to solve SDEs using Monte Carlo simulation
• understand the fundamental algorithms for the numerical solution of parabolic partial differential equations (PDEs)
• understand the binomial method for option pricing as a finite difference method, particularly its disadvantages
• be able to appreciate the importance of stability in numerical algorithms for PDEs
• understand numerical methods for the solution of nonlinear equations and some basic optimization techniques
• know the basics of relevant numerical methods, eg data fitting
• be able to illustrate the above by examples and exercises in Matlab

c) Programming in C++

• understand the language fundamentals of C and C++
• be able to use arrays, dynamic memory allocation and data input/output
• understand and be able to construct classes, illustrated by classes for complex numbers and matrix algebra
• be able to use numerical libraries.