Analysis and Computation for Finance
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 modelling, stochastic differential equations and 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 ECMM706 and in the dissertation ECMM720.
Full module specification
|Module title:||Analysis and Computation for Finance|
|Duration of module:||
Duration (weeks) - term 1: |
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.
ILO: Module-specific skills
- 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.
ILO: Discipline-specific skills
- 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.
ILO: Personal and key skills
- 4. show enhanced modelling, problem-solving and computing skills, and acquired tools that are widely used in financial modelling.
Learning activities and teaching methods (given in hours of study time)
|Scheduled Learning and Teaching Activities||Guided independent study||Placement / study abroad|
Details of learning activities and teaching methods
|Category||Hours of study time||Description|
|Scheduled learning and teaching activities||36||Lectures/supervised practical laboratory sessions/presentation of special topics|
|Guided independent study||114||Lecture and assessment preparation; wider reading|
Summative assessment (% of credit)
|Coursework||Written exams||Practical exams|
Details of summative assessment
|Form of assessment||% of credit||Size of the assessment (eg length / duration)||ILOs assessed||Feedback method|
|Written exam closed book||50||2 hours||All||None|
|Coursework problem sheet 2: approximation tools||8||All||Written|
|Coursework problem sheet 3: numerical matrix algebra||10||All||Written|
|Coursework problem sheet 4: computational ODEs and PDEs||10||All||Written|
|Coursework problem sheet 5: statistical modelling||12||All||Written|
|Coursework problem sheet 6: time series||10||All||Written|
Details of re-assessment (where required by referral or deferral)
|Original form of assessment||Form of re-assessment||ILOs re-assessed||Timescale for re-assessment|
|All above||Written exam (100%)||All||August Ref/Def period|
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 40% 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.
- introduction to Matlab system and interface: matrix data objects; mathematical operations and functions;
- I/O control;
- graphical tools;
- plotting and data representation;
- approximation techniques: curve Ã¯Â¬ï¿½tting and related methods;
- numerical matrix algebra: review;
- numerical calculation of eigenvalues, eigenvectors, determinants and inversion;
- special topics in numerical modelling: condition number;
- matrix nearness;
- Matlab numerical linear algebra tools;
- practical, numerical modelling using Matlab;
- computational ODEs, PDEs and dynamical systems: series,transforms,splines and interpolation;
- Ã¯Â¬ï¿½nite differences, shooting methods and convergence;
- Matlab DE tools;
- practical use of Matlab;
- statistical modelling: introduction to statistical models, parametric versus non-parametric models;
- likelihood, Bayesian and resampling inferential approaches;
- Markov Chain Monte Carlo, (MCMC methods;
- examples of parametric models - linear and generalised linear models;
- examples of computer-intensive non parametric modelling;
- use of relevant software in practical data modelling;
- times series modelling: fundamentals;
- methods for time series analysis and forecasting.
Indicative learning resources - Basic reading
ELE – http://vle.exeter.ac.uk
An Introduction To Numerical Methods: a MATLAB Approach, Kharab A. & Guenther R.B., Chapman & Hall, 2012, 518.0285 KHA, ISBN 978-1439868997
Data Analysis & Graphics using R, Maindonald J. & Braun J., 2nd edition, Cambridge University Press, 2007, 001.6424 MAI, ISBN 9780521861168
Computational statistics handbook with MATLAB, Martinez W.L. & Martinez A.R., Chapman & Hall, 2001, 519.50285 MAR, ISBN 000-1-584-88229-8
Time Series Analysis and its applications With R Examples, Shumway, R H, Stoffer, D S, 2nd, Springer Texts in Statistics, 2006, ISBN 978-0387293172
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