00675 - Financial Mathematics (PARI)

Course contents

Learning outcomes

Business Mathematics presents math skills and knowledge that you can apply to solve financial problems. Finance plays a major role in our lives--car loans, mortgage payments, retirement plans, real estate investment--and knowing how to calculate the cost of borrowing or the return on investment is important to us. The course provides step-by-step guidance through sample problems and solutions related to banking, credit, basic finance and investment. You will also gain an understanding of financial instruments and terminology used in business finance such as compound interest, annuities and promissory notes.

Portfolio theory introduces the theory and practice of modern portfolio theory and its application to investment analysis. The subject introduces the foundations of investment decision making under uncertainty, utility theory and portfolio selection via the mean-variance approach. The capital asset pricing model and the single index model are also developed.

Course contents

Module 1

Time value of money. Compounding and discounting single sums: future value and present value, interest and discount factor. Simple interest. Compound interest and compound discount. Equivalent rates. Nominal and effective annual interest rates. Continuous compounding and discounting.

Annuities and loan repayment. Ordinary annuity and annuity due. The present value and the future value of an annuity. Perpetuities. Discounting of continuous cash flows. Amortization with constant instalments and with constant principal payments. Outstanding principal. Amortization plan. Adjustable-rate loans.

Financial project evaluation (under certainty). Methods for investment evaluation and choice. Discounted Cash Flow (DCF) and Internal Rate of Return (IRR): definition, properties and financial meaning. Annual Percentage Rate.

Module 2

Bond valuation and yield curve. Term structure of interest rates. Spot rates and forward rates. Yield to maturity. Duration.

Valuation of risky investments. Choice under uncertainty, expected value, expected utility, stochastic dominance. Mean-variance criterion. Risk and volatility. Value at Risk.

Portfolio Theory. Portfolio Selection: Markowitz Model. Single-index models. Capital Asset Pricing Model (CAPM)

Readings/Bibliography

Module 1

D. Lovelock, M. Mendel, A.L. Wright, An Introduction to the Mathematics of Money: Saving and Investing. Springer, 2007;

or

S.A. Broverman, Mathematics of Investment and Credit (3rd edition ), Actex Publications, 2004.

Module 2

Edwin J. Elton, Martin J. Gruber, Stephen J. Brown, William N. Goetzmann, Modern portfolio theory and investment analysis. John Wiley, 2006;

or

D.G. Luenberger, Investment Science, Oxford University Press, 1998.

Teaching methods

Classroom lessons

The exercises and problems presented and discussed in the classroom are essential to properly understand all the parts of the program. In the written exam, the student will be required to solve specific exercises using the tools and techniques learnt in the classroom

Assessment methods

The examination consists of a written part and an oral part

The written exam is open book and students are welcome to bring their own reference material (books, notes, scientific calculator), for strictly personal use. No one will be allowed to exit the classroom after the written exam has begun.

Only students who pass the written part will be admitted to the oral exam, to be taken only in the scheduled dates. Students who do not take the oral examination in the scheduled date will be deemed to have withdrawn from the exam

The oral exam consists of two phases

A a discussion of the written exam, during which the student will be required to justify his/her answers to the exercises

B an interview about the main theoretical results, their applications, and topics which require a more in-depth knowledge of the subject.

Students are allowed to stop the oral exam just after phase A, if they estimate that their overall performance should not be worth more than 18/30

Teaching tools

• chalk
• blackboard
• transparencies
• PC connected projector

Office hours

See the website of Franco Nardini