00675 - Financial Mathematics

Learning outcomes

The aim of the course is to provide the fundamentals of Mathematical Finance. In particular, students will be able to understand and evaluate some financial contracts that are usually faced in business management. Some simple stategies for risk control and diversification will be presented

Course contents

Basic principles of financial mathematics: simple/commercial convention versus compound/instantaneous ones. Annuities. Perpetuities. Debt amortization. Evaluation of a generic financial transaction: NPV, IRR.

Fixed income market:term structure of interest rate, spot rates, forward rates, yield-to-maturity, duration. Complete and incomplete markets.

Valuation of risky investments. Expected utility. Stochastic dominance. Mean-variance. Risk and volatility. Value-at-Risk. Markowitz model for portfolio allocation. Capital Asset Pricing Model (CAPM

Readings/Bibliography

Giacomo Scandolo, Matematica Finanziaria. AMON Edizioni, 2013.

Giacomo Scandolo, Matematica Finanziaria. Esercizi svolti. AMON Edizioni, 2013.

Other suggested textbooks:

F. Cacciafesta, Lezioni di matematica finanziaria classica e moderna, Ed. Giappichelli Torino

Riccardo Cesari. Introduzione alla Finanza Matematica - Concetti di base, tassi, obbligazioni (2 Ed.), McGraw-Hill, 2012;

Riccardo Cesari. Introduzione alla Finanza Matematica – Mercati Azionari, Rischi e Portafogli (2 Ed.), McGraw-Hill, 2012;

D.G. Luenberger. Introduzione alla matematica finanziaria. Apogeo - Maggioli Editore, 2015.

Teaching methods

Lectures and exercises. Each topic is presented along with several examples and exercises. Some additional exercises will be discussed during the tutorial classes which are strongly recommended.

A Lab classes will be organized within the first Module.

Assessment methods

Written exam (duration 2 hours) consisting of short exercises and one or two more complex problems. Please note that the relevant topics will be always proposed in the written exam.

The first call will consist of two separate written exams, each counting for 50% of the final assessment.

The use of textbooks, notes, tablets, cell-phones, etc. is not allowed. Do not forget to bring a calculating machine.

Further information on the exam will be provided during the first lecture of each module.

Teaching tools

Slides. A list of exercises and some Excel speadsheets will be made available.

Office hours

See the website of Rossella Agliardi

See the website of Marco Antonio Boschetti