Methods for Stochastics and Finance

Module description

The module explores a diverse range of mathematical topics, emphasising their applications to financial modelling. The topics covered will range from matrix algebra to differential systems and stochastic calculus. This module will play an important role in underpinning the mathematical and computational methods needed for the subsequent modules in the financial mathematics MSc programme.

Full module specification

Module title:Methods for Stochastics and Finance
Module code:ECMM702
Module level:M
Academic year:2014/5
Module lecturers:
  • Dr Mark Holland - Convenor
Module credit:15
ECTS value:


Duration of module: Duration (weeks) - term 1:


Duration (weeks) - term 2:


Duration (weeks) - term 3:


Module aims

The module aims to engender an understanding of the mathematics useful for the theory of financial modelling and financial derivatives. It will also develop the students' mathematical ability and reasoning skills.

ILO: Module-specific skills

  • 1. demonstrate a competence in a broad range of methods for tackling mathematical problems, including solving differential equations, finding series and transforms, linear algebra methods, methods in advanced probability and stochastic calculus.

ILO: Discipline-specific skills

  • 2. identify the appropriate mathematical tools required to tackle complex mathematical problems.

ILO: Personal and key skills

  • 3. present and communicate your ideas in a mature and methodical manner.

Learning activities and teaching methods (given in hours of study time)

Scheduled Learning and Teaching ActivitiesGuided independent studyPlacement / study abroad

Details of learning activities and teaching methods

CategoryHours of study timeDescription
Scheduled learning and teaching activities 33Lectures/workshops
Guided independent study117Guided independent study

Formative assessment

Form of assessmentSize of the assessment (eg length / duration)ILOs assessedFeedback method
Not applicable

Summative assessment (% of credit)

CourseworkWritten examsPractical exams

Details of summative assessment

Form of assessment% of creditSize of the assessment (eg length / duration)ILOs assessedFeedback method
Written exam – closed book502 hours1,2In accordance with CEMPS policy
Coursework – example sheet 110500 words -10 hours1,2,3Written/tutorial
Coursework – example sheet 210500 words -10 hours1,2,3Written/tutorial
Coursework – example sheet 310500 words -10 hours1,2,3Written/tutorial
Coursework – example sheet 410500 words -10 hours1,2,3Written/tutorial
Coursework – example sheet 510500 words -10 hours1,2,3Written/tutorial

Details of re-assessment (where required by referral or deferral)

Original form of assessmentForm of re-assessmentILOs re-assessedTimescale for re-assessment
All aboveWritten exam (100%)AllAugust 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.

Syllabus plan

- approximation: polynomial approximation;
- Chebyshev polynomials, function approximation;
- matrix algebra: special matrices;
- systems of equations;
- matrix inversion;
- factorisation;
- eigenvectors/eigenvalues;
- ortogonal matrices and diagonalisation;
- ODEs and PDEs: finite differences;
- single-step methods;
- initial value and boundary value problems;
- eigenvalue problems;
- Laplace's equation and the diffusion equation;
- probability models: random variables;
- distributions;
- conditional probability and Bayes theorem;
- examples of probability modelling applications;
- Stochastic calculus: introduction to Ito calculus and stochastic differential equations;
- simulation and numerical solution of stochastic differential equations.

Indicative learning resources - Basic reading


  1. Applied Numerical Analysis,Gerald C.F. & Wheatley P.O.,7th,Anderson-Wesley,2004,519.4 GER,978-8131717400
  2. Elementary stochastic calculus with finance in view,Mikosch T.,World Scientific,1998,519.23 MIK,000-9-810-23543-7
  3. Computational statistics handbook with MATLAB,Martinez W.L. & Martinez A.R.,,Chapman & Hall,2001,519.50285 MAR,000-1-584-88229-8
  4. An Introduction To Numerical Methods: a MATLAB Approach,Kharab A. & Guenther R.B.,3rd,Chapman & Hall,2002,518.0285 KHA,978-1439868997

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