78355 - Quantitative Finance

Course Unit Page


This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

Quality education Decent work and economic growth

Academic Year 2023/2024

Learning outcomes

The purpose of this course is to provide some prerequisites to financial economics. Basics topics such as the term structure of interest rates, bond pricing and stock market functioning will be presented. The basics of securities trading (including trading platforms, market participants and the life-cycle of an order) will be analyzed with quantitative techniques to show whether security markets can be sufficiently good and fast at aggregating many bits of information and using them to price assets. Lab classes will complement the lectures, so that students will be able to work with financial data at the end of the course.

Course contents

The basic theory of interest: Compounding and discounting: future value and present value, interest and discount factor. Simple interest and compound interes. Nominal and effective annual interest rates.

Annuities: 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. Discounted Cash Flow (DCF) and Internal Rate of Return (IRR). Annual Percentage Rate.

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. Mean-variance criterion. Risk and volatility.

Portfolio Theory. Portfolio Selection: Markowitz Model. Two-fund theorem. One-fund theorem and tangency portfolio.


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

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

Teaching methods

The lectures will be given at the blackboard and by using slides. Moreover they will be structured in theoretical parts, examples and exercises.

Assessment methods

Written exam with exercises and questions. Students are expected to know the basic quantitative methods discussed during lectures and to critically discern the limitations of the models employed in the analysis.

In case online exams will be envisaged by the University of Bologna, the structure of the written exam is the same. The exam will be run through Zoom and Exams Online (EOL). Detailed instructions on how to manage and hand in the online exam are available on the course page on the VIRTUALE platform.

The maximum possible score is 30 cum laude, in case all answers are correct, complete and formally rigorous.

The grade is graduated as follows:

<18 failed
18-23 sufficient
24-27 good
28-30 very good
30 e lode excellent

Teaching tools

Slides, specialized articles and other didactic material will be made available.

Office hours

See the website of Fabrizio Lillo