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 MATH484
Coordinator Dr Deshpande
Mathematical Sciences
Amogh.Deshpande@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2016-17 Level 7 FHEQ First Semester 15

Aims

1.    To provide a computational background for modelling various continuous and discrete financial problems.

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

3.    To provide an in-depth, systematic and critical understanding of selected significant topics at the intersection of numerical analysis theory, Monte Carlo methods, and difference methods in PDEs, together with the related research issues.


Learning Outcomes

At the end of the module students should have:

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

2.    The ability to formulate computational models for the purpose of programming and answering particular financial questions.

3.    The ability to use appropriate tools and techniques in the context of a particular financial model. 

4.    The ability to read, understand and communicate research literature in the fields of numerical analysis, stochastic analysis and financial mathematics.

5.    The ability to recognise potential research opportunities and research directions.


Syllabus
1  1

Basic concepts used in numerical computing enviroment (i.e. MatLab functions to deal with Asset Pricing, Black-Scholes model etc).

Basics of Numerical Anaysis:

  • 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 approximatation, polynomial interpolation, interpolation by cybic splines.

Numerical Integration: Deterministic and Monte Carlo Methods

  • Deterministic quadrature
  • Monte Carlo integration
  • Generating pseudorandom variates
  • Variance reduction techniques

Finite Difference Merthods 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:
Programme:FMMF Year:1

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
Written Exam  2.5 hours  First semester  100  Standard university policy    Assessment 1 Notes (applying to all assessments) Final written examination  
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes