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MODULE TITLE	Methods for Stochastics and Finance	CREDIT VALUE	15
MODULE CODE	MTHM002	MODULE CONVENER	Dr 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 the 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 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.
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;

- 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;

- techniques in probability: 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	33.00	Guided Independent Study	117.00	Placement / Study Abroad

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

DETAILS OF SUMMATIVE ASSESSMENT

Form of Assessment	% of Credit	Size of Assessment (e.g. duration/length)	ILOs Assessed	Feedback Method
Written exam – closed book	80	2 hours (Summer)	1,2,3	Written/verbal on request
Coursework - example sheet 1	10	500 words - 10 hours	1,2,3	Written/tutorial
Coursework - example sheet 2	10	500 words - 10 hours	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
Written Exam *	Written exam (2 hours)	All	August Ref/Def period
Coursework 1 *	Coursework 1	All	August Ref/Def period
Coursework 2 *	Coursework 2	All	August Ref/Def 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

ELE: http://vle.exeter.ac.uk

Reading list for this module:

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

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 10 July 2018	LAST REVISION DATE	Thursday 26 January 2023

KEY WORDS SEARCH	Stochastic; financial mathematics; matrices; dissemination equations; approximation theory.

MTHM002 - Methods for Stochastics and Finance (2023)