# Mathematics

## MTHM003 - Analysis and Computation for Finance (2019)

MODULE TITLE CREDIT VALUE Analysis and Computation for Finance 15 MTHM003 Dr Frank Kwasniok (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 weeks 0 0
 Number of Students Taking Module (anticipated) 49
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/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.

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; [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].

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 Written/verbal on request
Coursework – problem sheet 1: Financial Data 15 8-12 hours All Written comments on script.
Coursework – problem sheet 2: Numerical 15 8-12 hours All Written comments on script.
Coursework – problem sheet 3:Stochastic Analysis in Finance 20 8-12 hours All Written comments on script.

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 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.

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