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: fairness condition as pillar for the evaluation, 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

Jansen J., Manca R., Volpe E., Mathematical Finance: Deterministic and Stochastic models, 2009, Wiley

Teaching methods

Theoretical lessons will be support by applied examples of discussed models to incite students to find themselves the explicit solutions of the theoretical problems applying the correct mathematical instruments.

Assessment methods

The learning test consists in a written exam to solve in 2 hours and concerning the different modules.   

The exam is mainly composed by many exercises and applied theoretical questions. It is attributed on average 2/3 points both to each exercise and theoretical question.

During the exam it is permitted to use the calculator and to consult books. The students pass the exam with a score not lower than 18 points.

The students can ask also for an oral exam about all the programme of the course. The final grade will be the average of the oral and the witten exam's grade of the two modules.

The final grade is recorded only if approved by the student.

 

Teaching tools

Teaching tools will be blackboard and slides.

Office hours

See the website of Silvia Romagnoli

See the website of Matteo Doti