Università degli Studi di Perugia

Skip to content

Unit MATHEMATICAL MODELS FOR FINANCIAL MARKETS

Course
Finance and quantitative methods for economics
Study-unit Code
A000200
Location
PERUGIA
Curriculum
Finanza ed assicurazione
Teacher
Davide Petturiti
Teachers
  • Davide Petturiti - Didattica Ufficiale
Hours
  • 63 ore - Didattica Ufficiale - Davide Petturiti
CFU
9
Course Regulation
Coorte 2019
Offered
2019/20
Learning activities
Caratterizzante
Area
Matematico, statistico, informatico
Sector
SECS-S/06
Type of study-unit
Obbligatorio (Required)
Type of learning activities
Attività formativa monodisciplinare
Language of instruction
English
Contents
*) Probabilistic tools necessary to the understanding of the course
1) Generalities on financial options
2) The Binomial model
3) The Black and Scholes model
4) Pricing of interest rate sensitive contracts
Reference texts
Lecture notes in English will be provided during the course.

The reference books are:

(Italian) G. Castellani, M. De Felice, F. Moriconi, Manuale di finanza – III. Modelli stocastici e contratti derivati, il Mulino, Bologna, 2006

(English) J.C. Hull, Options, Futures and Other Derivatives, 9th edition, Pearson, 2015
Educational objectives
At the end of the course the student will understand the logic of derivative contracts (in particular, forward contracts and options) and their pricing under uncertainty. He/she will be able to understand and use the most known stochastic pricing models based on the no-arbitrage principle, both in discrete and continuous time.
Prerequisites
The student must have basic knowledge of calculus, financial mathematics and probability theory covered in the Bachelor's courses: Matematica generale, Matematica finanziaria, Teoria matematica del portafoglio, Statistica. It is desirable that the student has passed the Master's course: Mathematical methods for risk management.
Teaching methods
The course is organized in face-to-face lectures and in-class exercises.
Other information
Students can ask for further explanations (individually or in small groups) during lecturer's office hours, available at: https://sites.google.com/site/davidepetturiti/.
Learning verification modality
The exam consists in a written and an oral test. To access the oral test, the student has to get a mark of at least 15/30. Those students with a mark ranging between 15/30 and 18/30 in the written test have to take the oral exam in the same call of the written exam.
Extended program
The programme of the course will be developed jointly with a recall to probabilistic tools necessary to the understanding of the topics of the course, such as: random variables and probability distributions, basic notions on (discrete and continuous time) stochastic processes, conditional expectation and martingales, Binomial processes and Brownian motions, stochastic differential and Ito's lemma. The course covers the following topics:

1) Generalities on financial options:
- Forward contracts, European and American option contracts: characterization
- Put-call parity
- Main types of option contracts
- Embedded options: corporate zero coupon bonds
- Embedded options: stock investments with a guaranteed minimum

2) The Binomial model:
- Binomial valuation: one-period scheme
- Replicating portfolio and risk-neutral probabilities
- The role of the no-arbitrage principle and of risk-neutral probabilities
- Two-period scheme
- Risk-neutral valuation and self-financing replication strategy
- Valuation formulas for European call and put options in the multi-period scheme
- The Delta
- Practical use of the Binomial model
- The Black and Scholes model as limit of the Binomial model

3) The Black and Scholes model:
- Hypotheses behind the model and the dynamics of the stock price
- Hedging argument and valuation equation
- Black and Scholes formulas for European call and put options
- Analysis of the Black and Scholes formulas
- Integral form solution and risk-neutral valuation
- Delta hedging
- Options on dividend paying stocks: deterministic dividend stream and deterministic dividend yield
- Foreign exchange options: the Garman and Kohlhagen model

4) Valuation of interest rate sensitive contracts:
- A recall on the term structure of interest rates
- A class of continuous-time one-factor models
- The Cox, Ingersoll and Ross model
- The Vasicek model
Go top
Table of content
×