00675 - Financial Mathematics

Course contents

Module 1

Time value of money.  Compounding and discounting: 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

S.A. Broverman, Mathematics of Investment and Credit (5th edition ), Actex Publications, 2010.

A separate solutions manual for the text exercises is:

S.A. Broverman, Mathematics of Investment and Credit, Solutions Manual  (5th edition ), Actex Publications, 2010.

Module 2

Edwin J. Elton, Martin J. Gruber, Stephen J. Brown, William N. Goetzmann, Modern portfolio theory and investment analysis, 9th edition, John Wiley, 2014;

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 exam (duration: 1 hour and a half) and an oral exam.

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.

Students who pass the written part will be admitted to the oral exam, which can be taken only in the scheduled dates. Students who select not to take the oral examination in the scheduled date will be given the grade of the written exam, up to a maximum of 24/30.

Office hours

See the website of Roberto Dieci