Study information

Methods for Stochastics and Finance - 2024 entry

MODULE TITLEMethods for Stochastics and Finance CREDIT VALUE15
MODULE CODEMTHM002 MODULE CONVENERDr Piotr Slowinski (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 weeks 0 0
Number of Students Taking Module (anticipated) 58
DESCRIPTION - summary of the module content

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.

 

AIMS - intentions of the module

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

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 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.

Discipline Specific Skills and Knowledge

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

Personal and Key Transferable / Employment Skills and Knowledge

3. present and communicate your ideas in a mature and methodical manner
SYLLABUS PLAN - summary of the structure and academic content of the module

Matrix algebra: 

  • special matrices;
  • systems of equations;
  • matrix inversion;
  • factorisation (e.g. LU factorization and Cholesky factorization);
  • eigenvectors/eigenvalues;
  • orthogonal 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.

Techniques in probaility: 

  • sets, measure, random variables, distributions;
  • probability models and introduction to stochastic processes;
  • Markov chains and random walks;
  • almost sure convergence and Borel Cantelli Lemmas.

Stochastic calculus:

  • introduction to Ito calculus and stochastic differential equations;
  • simulation and numerical solution of stochastic differential equations.
LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
Scheduled Learning & Teaching Activities 33 Guided Independent Study 117 Placement / Study Abroad 0
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Scheduled learning and teaching activities 22 Lectures
Scheduled learning and teaching activities 11 Workshops
Guided independent study 117 Guided independent study

 

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
SUMMATIVE ASSESSMENT (% of credit)
Coursework 0 Written Exams 100 Practical Exams 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Coursework 1 50 2-5 questions on matrix algebra and techniques in probability 1,2,3 Written/tutorial
Coursework 2 50 2-5 questions on ODEs, PDEs and stochastic calculus 1,2,3 Written/tutorial

 

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
Coursework 1 * Coursework 1 All Referral/deferral period
Coursework 2 * Coursework 2 All Referral/deferral period

*Please refer to reassessment notes for details on deferral vs. Referral reassessment

 

RE-ASSESSMENT NOTES

Deferrals: Reassessment will be by coursework and/or written exam in the deferred element only. For deferred candidates, the module mark will be uncapped.

Referrals: Reassessment will be by a single written exam worth 100% of the module only. As it is a referral, the mark will be capped at 50%. 

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

Basic reading:

  • Gerald C.F. & Wheatley P.O, Applied Numerical Analysis, 7th edition, Anderson-Wesley, 2004   978-8131717400 
  • Mikosch T. Elementary stochastic calculus with finance in view ,World Scientific, 1998   000-9-810-23543-7
  • Martinez W.L. & Martinez A.R.   Computational statistics handbook with MATLAB,Chapman & Hall , 2001   000-1-584-88229-8
  • Kharab, A. and Guenther, R.B.  An Introduction To Numerical Methods: A MATLAB Approach,Chapman & Hall , 2012   978-1439868997     

Reading list for this module:

Type Author Title Edition Publisher Year ISBN
Set Gerald C.F. & Wheatley P.O. Applied Numerical Analysis 7th Anderson-Wesley 2004 978-8131717400
Set Mikosch T. Elementary stochastic calculus with finance in view World Scientific 1998 000-9-810-23543-7
Set Martinez W.L. & Martinez A.R. Computational statistics handbook with MATLAB Chapman & Hall 2001 000-1-584-88229-8
Set Kharab, A. and Guenther, R.B. An Introduction To Numerical Methods: A MATLAB Approach Chapman & Hall 2012 978-1439868997
CREDIT VALUE 15 ECTS VALUE 7.5
PRE-REQUISITE MODULES None
CO-REQUISITE MODULES None
NQF LEVEL (FHEQ) 7 AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Tuesday 12th March 2024 LAST REVISION DATE Friday 13th September 2024
KEY WORDS SEARCH Stochastic; financial mathematics; matrices; dissemination equations; approximation theory.

Please note that all modules are subject to change, please get in touch if you have any questions about this module.