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 |
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Year | CATS Level | Semester | CATS Value |
Session 2019-20 | Level 7 FHEQ | First Semester | 15 |
Aims |
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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 |
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(LO1) A critical awareness of current problems and research issues in thefields of numerical analysis for different financial problems. |
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(LO2) The ability to formulate computational models for the purpose ofprogramming and answering particular financial questions. |
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(LO3) The ability to use appropriate tools and techniques in the context of aparticular financial model. |
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(LO4) The ability to read, understand andcommunicate research literature in the fields of numerical analysis, stochasticanalysis and financial mathematics. |
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(LO5) The ability to recognise potential research opportunities and researchdirections. |
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(S1) Problem solving skills |
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(S2) Numeracy |
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(S3) IT skills |
Syllabus |
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Basicconcepts used in numerical computing environment (i.e. MatLab functions to deal withAsset Pricing, Black-Scholes model etc). Basics of 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 Integration: 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 |
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Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module. |
Pre-requisites before taking this module (other modules and/or general educational/academic requirements): |
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(s) (including Year of Study) to which this module is available on an optional basis: |
Assessment |
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EXAM | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
Exam There is a resit opportunity. This is an anonymous assessment. Assessment Schedule (When) :At end of the Semester | 150 minutes. | 70 | ||||
CONTINUOUS | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
Computer-based coursework There is a resit opportunity. Standard UoL penalty applies for late submission. This is not an anonymous assessment. Assessment Schedule (When) :During the Semester | 30 |