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

A (mandatory) written exam, possibly followed by an (optional) oral examination.

The written exam consists of a number of exercises and problems of different levels of difficulty. In order to pass the written exam successfully, students need to properly frame the assigned problems, and to correctly and effectively apply the basic and advanced techniques of financial calculus learnt in the course.

The oral examination (requiring that the written part has been passed with a "sufficient" grade, at least 18/30) is optional. It must be regarded as a possible integration to the written exam, at the student's request. As such, it may affect the final grade both positively and negatively. In the absence of the oral examination, the grade of the written exam will be recorded as the final grade.

Office hours

See the website of Roberto Dieci