84553 - Financial Mathematics

Learning outcomes

The aim of the course is to provide the mathematics of the fundamental laws governing financial contracts. In particular, the course covers the different types of interest to compute present and accumulated values for different streams of cash flows. Applications include annuities, debt retirement methods, mortgages, bond and stock pricing, capital budgeting and the valuation of contingent claims.

Course contents

Basic principles of financial math: simple/commercial convention versus compound/istantaneous ones, the decomposability in the evaluation process.

Fundamental tools: annuities, periodicity and constancy of the payments, payments variable as an arithmetical/geometrical progression, discrete versus continuous annuities, perpetuities.

Simple and Complex financial transactions: sinking fund, amortization of a debt, reevaluation and indexation logic.

Fixed income market: term structure of interest rates, zero coupon bonds and fixed/indexed coupon bonds (floater, reverse floater), swap contracts.

Immunization.

Readings/Bibliography

Romagnoli S., Mathematical Finance- Theory, 2019, Esculapio

Romagnoli S., Mathematical Finance-Practice, 2019, Esculapio

Teaching methods

Theoretical lessons with exercises

Assessment methods

The final exam is written and should be solved in 2 hours. It is mostly made of exercises, with also a few theoretical questions.

It is possible to take it as two midterms, with the final grade being the average of the two marks.

During the exam it is possible to use the calculator (students are encouraged to bring it), as long as it is a device unable to connect to the internet.

The passing grade is 18/30.

Teaching tools

Slides, exercises, class notes.

Office hours

See the website of Amia Santini