00675 - Financial Mathematics

Academic Year 2010/2011

  • Docente: Roberto Dieci
  • Credits: 8
  • SSD: SECS-S/06
  • Language: Italian
  • Teaching Mode: Traditional lectures
  • Campus: Rimini
  • Corso: First cycle degree programme (L) in Business Economics (cod. 0909)

Learning outcomes

The course aims at providing the tools and skills needed to correctly represent and solve common financial problems

The course deals, in particular, with future and present values, interest rates and discount rates, the valuation of investments, the analysis of bond yields, and the term structure of interest rates. It also provides an introduction to the basic concepts of Finance, in particular the Mean-Variance approach to the choice under uncertainty and the Portfolio Selection problem.

Course contents

Module 1

Time value of money.  Compounding and discounting single sums: future value and present value, interest and discount factor. Simple interest. Compound interest and compound discount. Equivalent rates. Nominal and effective annual interest rates. Continuous compounding and discounting.

Annuities and loan repayment. Ordinary annuity and annuity due. The present value and the future value of an annuity. Perpetuities. Discounting of continuous cash flows. Amortization with constant instalments and with constant principal payments. Outstanding principal. Amortization plan. Adjustable-rate loans.

Financial project evaluation (under certainty). Methods for investment evaluation and choice. Discounted Cash Flow (DCF) and Internal Rate of Return (IRR): definition, properties and financial meaning. Annual Percentage Rate.

Bond valuation and yield curve. Term structure of interest rates. Spot rates and forward rates. Yield to maturity. Duration.

 

Module 2

Valuation of risky investments. Choice under uncertainty, expected value, expected utility, stochastic dominance. Mean-variance criterion. Risk and volatility. Value at Risk.

Portfolio Theory. Portfolio Selection: Markowitz Model. Single-index models. Capital Asset Pricing Model (CAPM).

Futures and Options.  Forward and futures contracts. Option Pricing: the binomial model.

Readings/Bibliography

Module 1

S.A. Broverman, Mathematics of Investment and Credit (5th edition ), Actex Publications, 2010.

A separate solutions manual for the text exercises is:

S.A. Broverman, Mathematics of Investment and Credit, Solutions Manual  (5th edition ), Actex Publications, 2010.

The previous edition (4th edition, 2008) can be used as well

 

Module 2

Edwin J. Elton, Martin J. Gruber, Stephen J. Brown, William N. Goetzmann, Modern portfolio theory and investment analysis, 7th edition, John Wiley, 2007;

or

D.G. Luenberger, Investment Science, Oxford University Press, 1998.

Teaching methods

Classroom lessons

The exercises and problems presented and discussed in the classroom are essential to properly understand all the parts of the program. In the written exam, the student will be required to solve specific exercises using the tools and techniques learnt in the classroom

Assessment methods

The examination consists of a written part and an oral part

The written exam is open book and students are welcome to bring their own reference material (books, notes, scientific calculator), for strictly personal use. No one will be allowed to exit the classroom after the written exam has begun.

Only students who pass the written part will be admitted to the oral exam, to be taken only in the scheduled dates. Students who do not take the oral examination in the scheduled date will be deemed to have withdrawn from the exam

The oral exam consists of two phases

A   a discussion of the written exam, during which the student will be required to justify his/her answers to the exercises

B an interview about the main theoretical results, their applications, and topics which require a more in-depth knowledge of the subject.

Students are allowed to stop the oral exam just after phase A, if they estimate that their overall performance should not be worth more than 18/30

Office hours

See the website of Roberto Dieci