Analysis and Computation for Finance - 2019 entry

On this module, you will get the chance to use the popular computer package Matlab and other relevant modelling software. We will cover topics from linear algebra, differential equations, statistical/probabilistic modelling, stochastic differential equations,

an introduction to time series analysis, and use these to demonstrate the versatility and capabilities of such packages in the application of modern numerical modelling techniques. The background and skills you will obtain in this module will be useful in the Financial Mathematics module MTHM006 Mathematical Theory of Option Pricing and in the dissertation ECMM721 Advanced Mathematics Project.

Computer packages such as Matlab are playing an increasing role in implementing the models arising from theoretical ideas in mathematical finance. This module aims to give you an understanding of the modern methods of numerical approximation and financial modelling. Using Matlab and other relevant software, you will develop practical skills in the use of computers in financial modelling.

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge:
1 demonstrate expertise in the use of Matlab and R widely used both inside and outside the academic community and be able to use these to model challenging mathematical problems.
Discipline Specific Skills and Knowledge:
2 tackle a wide range of mathematical problems using modern numerical methods;
3 model realistic situations and also understand the principles underlying the techniques and when they are applicable.
Personal and Key Transferable/ Employment Skills and  Knowledge:
4 show enhanced modelling, problem-solving and computing skills, and acquired tools that are widely used in financial modelling.

- Introduction to Matlab system and interface: matrix data objects; mathematical operations and functions; [week 1]

- Advanced Matlab operations: I/O control; programming; graphical tools; plotting and data representation; [week 1-2]

- Applications of Matlab: analysis of financial data and introduction to simple financial models;  approximation techniques such as curve fitting; simple numerical matrix algebra: numerical calculation of eigenvalues, eigenvectors, determinants, inversion and decompositions; [week 2-3]

- Special topics in numerical linear algebra: condition number; matrix nearness; Matlab numerical linear algebra tools; practical, numerical modelling using Matlab; [week 3-4]

- Computational ODEs, PDEs and dynamical systems: series,transforms, splines and interpolation; finite differences and their convergence;  Matlab DE tools; [week 4-5]

- Practical use of Matlab to PDE, ODE and dynamical system models. [week 5-6]

- Statistical and probabilistic modelling: introduction to statistical and probability modelling; Simulation and understanding stochastic processes using Matlab. Applications to simple financial models, e.g. Markov chain models and random walks. [week 6-8]

- An introduction to times series modelling: fundamentals and financial applications. e.g. autoregressive processes and their

use in financial modelling. [week 8-10]

-  Stochastic differential equations and their numerical solution: numerical Ito integration, Euler schemes for numerical solution, Monte Carlo simulation. Investigations into specific financial and asset pricing models. [week 10-11].

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.


If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 50% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

ELE – http://vle.exeter.ac.uk

Reading list for this module: