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Financial Mathematics

Lecturers

GHEZZI LUCA

Aim of the course

This course concerns the application of scientific tools to the investment activity. It deals with some of those scientific tools (models and procedures) that support financial decisions in the fields of

• the appraisal and comparison of investment projects;

• the appraisal, comparison and design of financial contracts;

• the management of financial risks.

There are two aims - to develop the students’ ability to represent reality by using models and to familiarise them with financial mathematics, the latter being a premise to financial engineering; needless to say, financial mathematics is based in some circumstances on notions that can be expressed only in mathematical terms. As for the investment activity, the course leads students to improve their understanding of its workings as well as of some of its procedures, learning what to analyse and how to approach a financial problem. To establish a link to the professional practice

• when presenting each financial problem some connections are made, whenever possible, to the main features of the setting where it arises; for instance, when presenting stocks and bonds a brief examination is put forward of the financial markets which they are traded on;

• emphasis is placed on models and procedures which are referred to in the professional practice, where the computer is used through, for instance, an electronic spreadsheet.

The material covered in each unit progresses from the simplest concept to the more advanced one. First the fundamentals of financial mathematics are presented as well as its basic applications. The acquired notions are then used to examine such applicative problems as the appraisal of companies, the selection of investment projects, the valuation of bonds, the management of interest rate risk, the measurement of a term structure of interest rates, the management of a stock portfolio. To cover the last subject, use is made of simple notions of probability theory.

.Syllabus

1.

. Basics of Financial mathematics.

Financial principles: accumulation and discount of money (simple and compound interest). Equivalent rates of compound interest. Continuous compound interest. Consistent accumulation factors. Annuities and perpetuities with payments in arrear. Repayment of a loan in instalments.

2. Investment appraisal.

Gordon’s model for the valuation of a company. Investment plans. Net present value, internal rate of return and benefit-cost ratio criteria: definition and properties. Selection of a single investment project. Investment ranking in capital budgeting. Financial projections of a business plan on an electronic spreadsheet. Inflation and real interest rates.

3. Fixed income securities

Money and capital markets. Pure discount and fixed rate coupon bonds: definition and valuation. Yield to maturity. Price and credit risk. Yield-price relation. Duration and variability of a bond price. Duration of a bond portfolio. Immunisation of a bond portfolio against interest rate risk.

4 Term structure of interest rates

Yield curves. Term structure of interest rates: definition and measurement. Spot and forward rates of interest. Floating rate coupon bonds: definition and valuation.

5. Basics of stock management.

Asset return. Portfolio return. Random variables. Portfolio selection: mean-variance framework, representation of feasible portfolios and derivation of efficient portfolios, risk diversification, inclusion of a risk-free asset, one-fund theorem. Selected empirical evidence on the workings of stock markets. Overview of portfolio management in practice.

Examinations

Attenders will take a written exam at the end of the course. The exam for the remaining students is oral. Non-attenders might contact their lecturer for advice on how to go about this subject

Reading list

Luenberger, D.G., *Investment Science*, New York, Oxford University Press, 1998.

Additional references may be made available in class. Handouts (including some reminders on theory and a set of worked out exercises) are available at the International Office.

To take this course, students must be familiar with the basics of calculus, optimisation and

probabilitytheory

probabilitytheory