CORSO DI STUDIO: Corso di Laurea Magistrale in Banca e Finanza

a.a. 2015/2016

Denominazione insegnamento/Course Title

Financial Mathematics of Uncertainty

Lingua dell’insegnamento: inglese
Crediti e ore di lezione: 9 cfu; 72 ore

Moduli: NO

Settore scientifico disciplinare: SECS-S/06

Docente: Flavio Pressacco
Indirizzo email: flavio.pressacco@uniud.it
Pagina web personale: http://people.uniud.it/page/flavio.pressacco

Prerequisiti e propedeuticità/Requirements

Prerequisites: basics of mathematical analysis, financial mathematics of certainty and probability theory provided, for instance, in classes of general mathematics, financial mathematics and statistics in three-year degree of Business Administration, curriculum Banking and Finance
Preconditions: none

Conoscenze e abilità da acquisire/Knowledge and skills

This course aims to provide knowledge of quantitative methods and instruments useful to the assessment of financial products (basic and complex) in uncertain context and, more generally, the analysis and rational solution of several problems related to decision-making economical-financial issues.

The student must:
- Know the current terminology, both in Italian and in English, on the quantitative finance and risk theory
- Know the instrumentation and quantitative methods given
- Know how to use them in the description, analysis and solution of concrete economical-financial problems

Skills related to the disciplines

Evaluate products and financial instruments; describe and analyze random situations; describe, quantify and cover all types of financial risk.

Soft skills

Draw comparisons with other specialists and being able to dialogue with interlocutors (customers, …) who have other skills using so friendly but strict their specialized skills.

Upgrade capabilities

The knowledge acquired should enable the continuous updating (life long learning) during his working life in view of the proper use of any technique or institutional innovation in the field of quantitative finance.

Programma e contenuti dell'insegnamento/Course description

Summary

- Recall of probability theory
- Recall of stochastic processes
- Introduction to stochastic differential equations
- Single period binomial financial markets
- Arbitrage free pricing on single period binomial financial markets
- Price risk and interest rate risk on financial markets
- Theory of plain vanilla options
- Arbitrage free options pricing
- Introduction to interest rate options

Detailed program

- Recall of stochastic processes
Binomial processes
Sum of binomial random variables (additive binomial process)
Multiplicative binomial process
Continuous time processes
Wiener process
Diffusion process
Log-normal process

- Introduction to stochastic differential equations
Stochastic differential equations
Total stochastic differential
Ito’s Lemma

- Single period binomial financial markets
The single period asset return on binomial markets
Portfolios of assets on binomial market
Dominance between assets and portfolios on binomial markets
Arbitrage free markets
Risk neutral probability
Characteristic line of a single period market

- Arbitrage free pricing on single period binomial financial markets
Price as the present value of the risk neutral expectation

- Price risk and interest rate risk on financial markets
Multiperiod markets (big markets) and arbitrage free pricing
Big markets of the I, II, III type
Arbitrage free pricing of risky assets in big markets of the I and II type
Arbitrage free pricing of interest rate sensitive asset in big markets of the III type

- Theory of plain vanilla options
Put, Call, European and American options
The payoff at maturity of an option
Fundamental equation of option theory
Put-Call parity for European options
Support and intrinsic value for Put and Call options
Components of European options value
The time value
Interest premium or interest toll
American options
Early exercise on American options

- Arbitrage free options pricing
Arbitrage free pricing of European options on binomial market of the I type
Arbitrage free pricing of American options on binomial market of the I type
The backward induction
Early exercise opportunity
Hedging portfolio
Black-Scholes formula

- Introduction to interest rate options
Cap, Floor, Swap, Collar
Binomial trees for interest rate in multiperiod markets of the III type
Introduction to the pricing of an interest rate sensitive asset
Options on interest rates in multiperiod markets of the III type

Attività di apprendimento e metodi didattici previsti/ Teaching and Learning activities

During the course it will be used primarily by the teacher handouts available online and a textbook for some parts of the program.

The course will consist mainly of theoretical lectures, seasoned with some practical exercises.

Modalità di verifica dell'apprendimento/Examination

The examination consists of:
written and / or oral test, any intermediate tests, any project work.

Passing the written test with a rating of at least 15/30 is a necessary condition for admission to the oral test.

Testi / Bibliografia/Bibliography

- F. Pressacco- P. Stucchi, Lezioni di Matematica Finanziaria, FORUM, cap. 4 e appunti a cura del docente
- J. HULL, Opzioni, futures e altri derivati, Il Sole 24 Ore, 2000.
- Slides by the teacher available online.

Strumenti a supporto della didattica/Further readings and support material

Educational slides freely available on line.

Tesi di laurea/Thesis

Types of thesis: thesis theoretical and practical, presentation of case studies.

Note/Remarks

The course is designed to prepare students to deal with problems of a financial nature in the banking and insurance as well as managerial frameworks and is seen as a prerequisite to some quantitative finance courses taught in the same degree program.

There are no differences in program and/or examination among students regularly attending lessons and not.