84553 - FINANCIAL MATHEMATICS

Academic Year 2018/2019

  • Moduli: Silvia Romagnoli (Modulo 1) Fabio Della Marra (Modulo 2)
  • Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
  • Campus: Bologna
  • Corso: First cycle degree programme (L) in Economics and Finance (cod. 8835)

Learning outcomes

The aim of the course is to provide the mathematics of the fundamental laws governing Financial contracts as for example loan's amortization and sinking fund prospects. Particular attention will be adressed to bond market and to the valuation of risks coming from a shift of the term structure of interest rates. Immunization arguments will be proposed such that at the end of the course students will be able to discuss the Financial impact of a parameter variation and to compare alternative hedging strategies. Among these they will score the advantagies provided by index liked products and credit derivatives in risk management process.

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.
  • Basic options theory: an introduction to options, the distinction between a put and a call, the payoff of an option, put-call parity.
  • Readings/Bibliography

    Romagnoli S., Mathematical Finance- Theory, 2016, Esculapio

    Romagnoli S., Mathematical Finance-Practice, 2017, Esculapio

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

    Assessment methods

    The learning test consists in two written exams to solve in 3 hours and concerning the different modules.   

    The exams are mainly composed by 2 exercises and an applied theoretical question. During the exam, it is permitted to use the calculator and to consult books. It is attributed on average 10 points both to each exercise and to the 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 Fabio Della Marra