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# MA907 - Numerical Methods & Programming

• Module code: MA907
• Module name: Numerical Methods & Programming
• Department: Mathematics Institute
• Credit: 12, 15

## Module content and teaching

###### Principal aims

This module aims to provide both a theoretical and a practical understanding of numerical methods in finance, in particular those related to simulations of stochastic processes. In addition the module will give an introduction into programming. Students will be asked to analyse a model relevant for financial maths using MATLAB. A typical project contains 30-40 pages of model derivation, tables, graphs and diagrams illustrating the results and the analysis of numerical results. The project also has an appendix with relevant MATLAB codes written by the student. This module aims to provide both a theoretical and a practical understanding of numerical methods in finance, in particular those related to simulations of stochastic processes. In addition the module will give an introduction into programming.

###### Principal learning outcomes

"Application of advanced methods of linear algebra to qualitative and numerical analysis of models of Mathematical Finance; Understanding of stability of numerical schemes of linear algebra, relation between the relative error of the scheme and the conditioning number, convergence criteria of recursive numerical schemes; Understanding of basic limiting laws of probability theory in the context of mathematical finance; Ability to apply probability theory and linear algebra to extract specific predictions from the given financial model. -Understanding of CRR difference equation and European, American, Barrier options pricing using binomial and trinomial trees; Understanding of basic numerical schemes for solving differential and stochastic differential equations, their stability, complexity and convergence. Ability to choose an appropriate numerical scheme for the problem at hand; The ability to use stochastic calculus to bring the formulate mathematical models of price fluctuations and analyse their consequences with application to quantitative finance; Demonstrate introductory knowledge of C++; Demonstrate analytical skills and the ability to evaluate critically mathematical models and the numerical solution methods used in the quantitative finance; Understanding of strengths and weaknesses of various mathematical models of price fluctuations via comparison with real market data; Understanding of applicability conditions of various mathematical theories used in mathematical finance; Familiarity with basic applications of linear algebra, probability theory and the theory of differential equations to mathematical finance; Good understanding of principles underlying numerical schemes used to analyse models of mathematical finance. The ability to choose the appropriate numerical scheme for the problem at hand basing on the scheme’s stability, order of convergence, required numerical precision of the final answer; The ability to recognize the advantages and/or shorcomings of the quantitative model of mathematical finance at hand; The ability to choose an appropriate numerical scheme for the analysis of the model."

###### Departmental link

http://www2.warwick.ac.uk/fac/cross_fac/financial_maths/warwickmsc/outline

###### Other essential notes

Available for MSc Financial Mathematics students

## Module assessment

Assessment group Assessment name Percentage
12 CATS (Module code: MA907-12)
C (Assessed/examined work) Programming Project 50%
2 hour examination (January) 50%
D (Assessed/examined work) Programming Project 40%
2 hour examination (January) 60%
15 CATS (Module code: MA907-15)
C (Assessed/examined work) Programming Project 50%
2 hour examination (January) 50%
D (Assessed/examined work) Programming Project 40%
2 hour examination (January) 60%

## Module availability

This module is available on the following courses:

###### Core
• Postgraduate Taught Financial Mathematics (N3G1) - Year 1

N/A

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