Module Details
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
Title COMPUTATIONAL METHODS IN FINANCIAL MATHEMATICS
Code MATL484
Coordinator Dr S Mitra
Mathematical Sciences
Sovan.Mitra@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2016-17 Level 7 FHEQ First Semester 15

Aims

1.    To provide acomputational background for modelling various continuous and discretefinancial problems.

2.   To provide the basic tools and techniques in analysing and modelling continuousand discrete financial problems and to apply these tools and techniques toreal-world financial problems.

3.   To provide an in-depth, systematic and critical understanding of selectedsignificant topics at the intersection of numerical analysis theory, MonteCarlo methods, and difference methods in PDEs, together with the relatedresearch issues.



Learning Outcomes

A critical awareness of current problems and research issues in thefields of numerical analysis for different financial problems.

The ability to formulate computational models for the purpose ofprogramming and answering particular financial questions.

The ability to use appropriate tools and techniques in the context of aparticular financial model.

The ability to read, understand andcommunicate research literature in the fields of numerical analysis, stochasticanalysis and financial mathematics.

The ability to recognise potential research opportunities and researchdirections.


Syllabus
1 

Basicconceptsused in numerical computing environment (i.e. MatLab functions to deal withAsset Pricing, Black-Scholes model etc).

Basicsof Numerical Analysis:

  • Nature of numerical computation : Error analysis, order of convergence and computational complexity
  • Solving systems of linear equation : Direct and Iterative methods for solving systems of linear equations
  • Function approximation and interpolation : Ad hoc approximation, polynomial interpolation, interpolation by cubic splines .     
  • Numerical Integ ration: Deterministic and Monte Carlo Methods

  • Deterministic quadrature
  • Monte Carlo integration
  • Generating pseudorandom variates
  • Variance reduction techniques
  • Finite Difference Methods for Partial Differential Equations

  • Introduction and classification of PDEs
  • Numerical solution by finite difference methods

Applications

  • Option Pricing by Binomial and Trionomial Lattices, and Monte Carlo Methods (MatLab).
  • Option Pricing by Finite Difference Methods (MatLab)

 







 


Recommended Texts
Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.
Explanation of Reading List:

Pre-requisites before taking this module (other modules and/or general educational/academic requirements):
BSc Maths/Financial Maths 

Co-requisite modules:
 

Modules for which this module is a pre-requisite:
 

Programme(s) (including Year of Study) to which this module is available on a required basis:
MPFA - Financial & Actuarial Mathematics

Programme(s) (including Year of Study) to which this module is available on an optional basis:
 

Assessment
EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Unseen Written Exam  150  At end of the Semester  70  Yes    Exam Notes (applying to all assessments) Assessment 1: computer-based coursework Assessment 2: exam with rubric `Full marks will be awarded for correct answers to FIVE questions.' 
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Coursework    During the Semester  30  Yes  Standard UoL penalty applies  Computer-based coursework