MATH1510 Financial Mathematics I - University of Leeds

MATH1510 Financial Mathematics I

Jitse Niesen University of Leeds January ? May 2012

Description of the module

This is the description of the module as it appears in the module catalogue.

Objectives

Introduction to mathematical modelling of financial and insurance markets with particular emphasis on the time-value of money and interest rates. Introduction to simple financial instruments. This module covers a major part of the Faculty and Institute of Actuaries CT1 syllabus (Financial Mathematics, core technical).

Learning outcomes

On completion of this module, students should be able to understand the time value of money and to calculate interest rates and discount factors. They should be able to apply these concepts to the pricing of simple, fixed-income financial instruments and the assessment of investment projects.

Syllabus

? Interest rates. Simple interest rates. Present value of a single future payment. Discount factors.

? Effective and nominal interest rates. Real and money interest rates. Compound interest rates. Relation between the time periods for compound interest rates and the discount factor.

? Compound interest functions. Annuities and perpetuities.

? Loans.

? Introduction to fixed-income instruments. Generalized cashflow model.

? Net present value of a sequence of cashflows. Equation of value. Internal rate of return. Investment project appraisal.

? Examples of cashflow patterns and their present values.

? Elementary compound interest problems.

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Reading list

These lecture notes are based on the following books:

1. Samuel A. Broverman, Mathematics of Investment and Credit, 4th ed., ACTEX Publications, 2008. ISBN 978-1-56698-657-1.

2. The Faculty of Actuaries and Institute of Actuaries, Subject CT1: Financial Mathematics, Core Technical. Core reading for the 2009 examinations.

3. Stephen G. Kellison, The Theory of Interest, 3rd ed., McGraw-Hill, 2009. ISBN 978-007-127627-6.

4. John McCutcheon and William F. Scott, An Introduction to the Mathematics of Finance, Elsevier Butterworth-Heinemann, 1986. ISBN 0-75060092-6.

5. Petr Zima and Robert L. Brown, Mathematics of Finance, 2nd ed., Schaum's Outline Series, McGraw-Hill, 1996. ISBN 0-07-008203.

The syllabus for the MATH1510 module is based on Units 1?9 and Unit 11 of book 2. The remainder forms the basis of MATH2510 (Financial Mathematics II). The book 2 describes the first exam that you need to pass to become an accredited actuary in the UK. It is written in a concise and perhaps dry style.

These lecture notes are largely based on Book 4. Book 5 contains many exercises, but does not go quite as deep. Book 3 is written from a U.S. perspective, so the terminology is slightly different, but it has some good explanations. Book 1 is written by a professor from a U.S./Canadian background and is particularly good in making connections to applications.

All these books are useful for consolidating the course material. They allow you to gain background knowledge and to try your hand at further exercises. However, the lecture notes cover the entire syllabus of the module.

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MATH1510

Organization for 2011/12

Lecturer

Jitse Niesen

E-mail

jitse@maths.leeds.ac.uk

Office

Mathematics 8.22f

Telephone

35870 (from outside: 0113 3435870)

Lectures

Tuesdays 10:00 ? 11:00 in Roger Stevens LT 20 Wednesdays 12:00 ? 13:00 in Roger Stevens LT 25 Fridays 14:00 ? 15:00 in Roger Stevens LT 17

Example classes Mondays in weeks 3, 5, 7, 9 and 11, see your personal timetable for time and room.

Tutors

Niloufar Abourashchi, Zhidi Du, James Fung, and Tongya Wang.

Office hours

Tuesdays . . . . . . . . (to be determined) or whenever you find the lecturer and he has time.

Course work

There will be five sets of course work. Put your work in your tutor's pigeon hole on Level 8 of School of Mathematics. Due dates are Wednesday 1 February, 15 February, 29 February, 14 March and 25 April.

Late work

One mark (out of ten) will be deducted for every day.

Copying

Collaboration is allowed (even encouraged), copying not. See the student handbook for details.

Exam

The exam will take place in the period 14 May ? 30 May; exact date and location to be announced.

Assessment

The course work counts for 15%, the exam for 85%.

Lecture notes

These notes and supporting materials are available in the Blackboard VLE.

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