Introduction to Numerical Methods in Finance

8/18/2019 Introduction to Numerical Methods in Finance

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FE 1015

Numerical Methods I for Finance

Dr. Naleen GanegodaDepartment of MathematicsUniversity of Sri Jayewardenepura

2013/2014

B.Sc. in Financial Engineering - Diploma Level - FE 1015 Numerical Methods I for Finance

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Contents

IntroductionIntroduction to the courseLearning outcomes

SyllabusIntroduction to numerical methods

Needs of numerical methods in finance

Discussion session


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Introduction to the course

Main objective of this course is to address knowledge and skillsrelevant to numerical methods needed to quantify work in fi-nance field. Thus, your learning process should be designedwith both gaining the knowledge on numerical methods andapplying them in problem solving in finance field.


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Introduction to the course

Main objective of this course is to address knowledge and skillsrelevant to numerical methods needed to quantify work in fi-nance field. Thus, your learning process should be designedwith both gaining the knowledge on numerical methods andapplying them in problem solving in finance field.

To cater the above objectives we have,(i) 10 Lessons(ii) Worked examples(iii) Applications in finance(iv) Computer practical sessions (using MATLAB software)(v) Assignments(vi) MCQ question bank


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Learning outcomes

At the end of this course you will be able to

(i) identify numerical methods and the needs of them infinance(ii) identify sources of numerical errors and error propagation

(iii) quantify numerical errors in approximations(iv) identify iterative procedures to solve non-linear equations(v) distinguish different iterative methods and theirconcergence in solving non-linear equations(vi) identify basic concepts in interpolation

(vii) apply different methods of interpolation to makeapproximations(viii) analyse interpolating errors


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Learning outcomes ctd...

(ix) distinguish algebraic and numerical methods of solvingsystems of linear equations.(x) solve systems of linear equations numerically by direct anditerative methods(xi) quantify the errors in solving systems numerically

(xii) identify basic concepts of numerical differentiation andintegration(xiii) apply different numerical methods to evaluate derivativesand integrations

(xiv) determine errors associated with numericaldifferentiation and integration(xv) design MATLAB programs for numerical methods


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Syllabus

Lesson 1: Introduction to numerical methods and needs of numerical methods in finance

Lesson 2: Errors: Sources, Estimation and Analysis

Lesson 3: Numerical methods of solving non-linear equationsPart I - Introduction to iterative procedure

Lesson 4: Numerical methods of solving non-linear equationsPart II - Iterative Methods

Lesson 5: InterpolationPart I - Introduction to interpolating methods

Lesson 6: InterpolationPart II - Lagrange and Hermite interpolation,Divided diference

technique, Interpolating errorB.Sc. in Financial Engineering - Diploma Level - FE 1015 Numerical Methods I for Finance

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Syllabus ctd...

Lesson 7: Numerical methods of solving systems of linearequationsPart I - Preliminaries and direct methods

Lesson 8: Numerical methods of solving systems of linearequationsPart II - Error analysis and iterative methods

Lesson 9: Numerical Differentiation

Lesson 10: Numerical Integration


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Assesment criteria

Assignments/In-class exams (witten & practical) (40%)

End of semester written examination (60%)


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Lesson 1

Introduction to numerical methods and needs of

numerical methods in finance


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Introduction to numerical methods

The subject area of numerical methods consists of computa-tional approaches for solving mathematical problems. Rapiddevelopments in digital computing has underpined the develop-ment of numerical methods too. Thus, it provides easier andfaster ways of solving problems. In fact, numerical methods are

the definite alternatives if a problem cannot be solved analyti-cally or available algebraic methods to solve a problem are toocostly in terms of compuational time.


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Introduction to numerical methods

The subject area of numerical methods consists of computa-tional approaches for solving mathematical problems. Rapiddevelopments in digital computing has underpined the develop-ment of numerical methods too. Thus, it provides easier andfaster ways of solving problems. In fact, numerical methods are

the definite alternatives if a problem cannot be solved analyti-cally or available algebraic methods to solve a problem are toocostly in terms of compuational time.

Analysing errors is a major concern associated with numericalmethods. Usually, numerical methods provide approximationsto the desired true solution. Thus, it is important to at leasthave bounds on resulting errors.




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Introduction to numerical methods ctd...

Aspect of iterative procedures is also a major highlight in somenumerical methods. It incorporates a step by step convergencetowards the required solution according to a defined rule. Fastercomputing allows even to practice trial and error methodology

in applying iterative methods.




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Introduction to numerical methods ctd...

Aspect of iterative procedures is also a major highlight in somenumerical methods. It incorporates a step by step convergencetowards the required solution according to a defined rule. Fastercomputing allows even to practice trial and error methodology

in applying iterative methods.

Skills on designing computer programs is a very important as-pect to be developed in studying numerical methods. It eval-uates logical thinking abilities to formulate required algorithms

which ultimately highlightes essential component of computersimulation in any modern applied research.




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After the preliminary introduction on numerical methods, let us now

consider why we should learn numerical methods in association withfinance.

What are your thoughts? (discussion session)


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What are numerical in finance? (eg. quantitative factors)


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What are their forms? (eg. rates, integer values, values withdecimals, set/system/series of values, formula input/output,solutions of equations, etc.)


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What are the types of utilization? (eg. day-to-day financialtransactions, identifying trends in financial markets, researchlevel incorporations, etc.)


N d f i l h d i fi

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What are the types of utilization? (eg. day-to-day financialtransactions, identifying trends in financial markets, researchlevel incorporations, etc.)

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Introduction to Numerical Methods in Finance

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Transcript of Introduction to Numerical Methods in Finance