# Mathematics

## ECMM703 - Analysis and Computation for Finance (2015)

MODULE TITLE CREDIT VALUE Analysis and Computation for Finance 15 ECMM703 Dr Tim Jupp (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 weeks 0 0
 Number of Students Taking Module (anticipated) 21
DESCRIPTION - summary of the module content

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.

AIMS - intentions of the module

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.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

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.

SYLLABUS PLAN - summary of the structure and academic content of the module

- introduction to Matlab system and interface: matrix data objects; mathematical operations and functions;
- I/O control;
- programming;
- graphical tools;
- plotting and data representation;
- approximation techniques: curve ﬁtting and related methods;
- numerical matrix algebra: review;
- numerical calculation of eigenvalues, eigenvectors, determinants and inversion;
- decompositions;
- 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;
- ﬁnite 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.

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study 39 114
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled learning and teaching activities 24 Lectures Scheduled learning and teaching activities 15 Workshops Guided independent study 114 Guided independent study

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Not applicable

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams 50 50
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) 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 Time Scale for Re-reassessment
All above Written exam (100%) All August Ref/Def period

RE-ASSESSMENT NOTES

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.

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

ELE – http://vle.exeter.ac.uk