B5135 - MATHEMATICAL TOOLS AND SIMULATION TECHNIQUES

Learning outcomes

This course is designed to provide the student with an in-depth knowledge of Integral Calculus, Differential Equations and Multivariable Differential Calculus with a special emphasis on Extremum Problems. Students should view this course as a compendium of mathematical tools for several courses in their economic curriculum. The traditional class lectures will be complemented by Lab classes designed to train students in numerical solving of some specific problems and in simulation techniques. At the end of the course, the student will gain a better understanding of the mathematics behind some significant economic models and will be more proficient in building and developing practical solutions to some specialist applications.

Course contents

Basic principles of financial mathematics: simple/commercial convention versus compound/instantaneous ones. Annuities-certain: present values and accumulations. Deferred annuities. Perpetuities. Loan repayment schedules. Project appraisal and investment performance. NPV, IRR.

Fixed income market: term structure of interest rate, spot rates, forward rates, yield-to-maturity, duration. Italian sovereign bonds. Green finance: green bonds and sustainability-linked bonds.

Valuation of risky investments. Expected utility. Stochastic dominance. Mean-variance. Risk and volatility. Value-at-Risk. Markowitz model for portfolio allocation.

Financial derivatives: forward contracts, futures, options.

Readings/Bibliography

S. J. Garrett. An Introduction to the Mathematics of Finance. Butterworth-Heinemann. Second edition

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.

Assessment methods

Written exam (duration 60 minutes) 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, personal notes and other printed notes is allowed; tablets and cell-phones are 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.

The use of AI is forbidden during the exam and any use will constitute a violation of academic integrity.

Teaching tools

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

Office hours

See the website of Rossella Agliardi