First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Economics and Political Science
ECONOMICS AND FINANCE
Course unit
MATHEMATICS FOR FINANCIAL RISK AND DERIVATIVES
EPP6077357, A.A. 2018/19

Information concerning the students who enrolled in A.Y. 2018/19

Information on the course unit
Degree course Second cycle degree in
ECONOMICS AND FINANCE
EP2422, Degree course structure A.Y. 2017/18, A.Y. 2018/19
N0
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Degree course track BANKING AND FINANCE [001PD]
Number of ECTS credits allocated 9.0
Type of assessment Mark
Course unit English denomination MATHEMATICS FOR FINANCIAL RISK AND DERIVATIVES
Website of the academic structure http://www.economia.unipd.it
Department of reference Department of Economics and Management
E-Learning website https://elearning.unipd.it/economia/course/view.php?idnumber=2018-EP2422-001PD-2018-EPP6077357-N0
Mandatory attendance No
Language of instruction English
Branch PADOVA
Single Course unit The Course unit CANNOT be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge CLAUDIO FONTANA MAT/06

Mutuated
Course unit code Course unit name Teacher in charge Degree course code
EPP6077357 MATHEMATICS FOR FINANCIAL RISK AND DERIVATIVES CLAUDIO FONTANA EP2423

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses MAT/06 Probability and Mathematical Statistics 9.0

Course unit organization
Period First semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
hours
Hours of
Individual study
Shifts
Lecture 9.0 63 162.0 No turn

Calendar
Start of activities 01/10/2018
End of activities 18/01/2019

Examination board
Board From To Members of the board
2 Commissione A.A. 2018/19 01/10/2018 30/09/2019 FONTANA CLAUDIO (Presidente)
BURATTO ALESSANDRA (Membro Effettivo)
GROSSET LUCA (Membro Effettivo)

Syllabus
Prerequisites: A solid knowledge of basic mathematics, probability and statistics.
Target skills and knowledge: This course provides a rigorous introduction to asset pricing and quantitative finance. The first part of the course covers fundamental topics such as the time value of money and classical portfolio theory. The second part of the course consists of an introduction to financial derivatives and the modeling of asset prices, first in a discrete-time setting and then in a continuous-time setting. The relevant tools of stochastic calculus will be presented together with their financial applications.
Examination methods: Written exam
Assessment criteria: 100% final written exam
Course unit contents: A Brief Introduction to Financial Markets
– Exchange-traded markets and OTC markets
– Hedgers, speculators and arbitrageurs
The Monetary Value of Time
– Types of interest rates
– Bond pricing, yields and duration
– Net Present Value (NPV) and Internal Rate of Return (IRR)
Portfolio Theory
– Preferences and expected utility
– Two-securities portfolio selection
– N-securities portfolio selection
– Mean-variance (Markowitz) portfolio selection
– Portfolio frontier and efficient portfolios
– The Capital Asset Pricing Model (CAPM)
– The Sharpe ratio
Financial Derivatives
– Forwards and futures
– Options: European and American, vanilla and exotic
– The no-arbitrage principle and the law of one price
– Static strategies with options
– Put-Call parity
– General no-arbitrage bounds
The Binomial Model
– Absence of arbitrage
– Dynamic trading and hedging
– Pricing by hedging
– Risk-neutral probability measures
– Pricing by risk-neutral valuation
– American options: optimal exercise, hedging and pricing
– Law of large numbers and limit behavior
Brownian Motion and Stochastic Calculus
– An introduction to stochastic processes
– Definition and basic properties of the Brownian motion
– Martingales and Markov processes
– The stochastic integral
– Itô's formula
– Stochastic differential equations
The Black-Scholes-Merton (BSM) Model
– Geometric Brownian motion
– Dynamic trading and hedging in continuous time
– Absence of arbitrage
– Risk-neutral probability measures
– Changes of measure (the Girsanov theorem)
– The Feynman-Kač formula
– The Black-Scholes pricing formula
– PDE approach to the BSM model
– The Greeks
– Implied volatility
Planned learning activities and teaching methods: Presentation of mathematical models by teacher and exercises.
Textbooks (and optional supplementary readings)
  • John C. Hull, Options, Futures, and Other Derivatives (10th Edition). --: Pearson, 2017. Cerca nel catalogo
  • Tomas Björk, Arbitrage Theory in Continuous Time 3°ed. Oxford: Oxford University Press, 2009. Cerca nel catalogo
  • Barucci Emilio, Fontana Claudio, Financial markets theoryequilibrium, efficiency and information 2°ed. London: Springer, 2017. Cerca nel catalogo
  • Pascucci, Andrea, Calcolo stocastico per la finanzaAndrea Pascucci. Milano: Springer, 2009. Cerca nel catalogo

Innovative teaching methods: Teaching and learning strategies
  • Lecturing
  • Case study
  • Interactive lecturing