Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Study Plan
This information is intended exclusively for students already enrolled in this course.If you are a new student interested in enrolling, you can find information about the course of study on the course page:
Laurea magistrale in Banca e finanza - Enrollment from 2025/2026The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.
1° Year
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2° Year activated in the A.Y. 2015/2016
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Legend | Type of training activity (TTA)
TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.
Derivatives (2015/2016)
Teaching code
4S02483
Teacher
Coordinator
Credits
9
Language
Italian
Scientific Disciplinary Sector (SSD)
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES
Period
primo semestre dal Sep 28, 2015 al Jan 8, 2016.
Learning outcomes
The course is prepared for students which followed the courses “Stochastic Models for Finance” and “Mathematical Finance”. The Black-Scholes model is considered a prerequisite.
The objective of the course is to describe and analyze the main mathematical models used for the valuation of financial derivatives. The course is divided into four pillars, which correspond to the four main financial markets: interest rate derivatives, credit derivatives, equity derivatives and FX derivatives. The course will also introduce practical tools for the implementation of the mathematical models with standard scientific software, and the calibration of these models to market data.
Program
1. Interest rate derivatives
a. Absence of arbitrage and risk-neutral probabilities
b. FRA, swaps
c. Black's model: caps, floors, swaptions
d. Short term models: Vasicek, CIR
e. Forward measure
f. The “double curve” model
2. Credit derivatives
a. Exponential distribution
b. Poisson processes
c. Reduced form models for credit risk
d. Risky bonds evaluation
e. Credit default swaps
f. Credit Valuation Adjustment
3. Equity derivatives
a. The limitations of the Black & Scholes model
b. Greeks
c. Stochastic volatility in discrete time
d. Stochastic volatility in continuous time: Hull and White, Heston, SABR
e. Model free implied volatility: the VIX index
f. Multi-factor and jump-diffusion models
4. Derivati su valute
a. The Garman-Kolhagen formula
b. Currency swaps
c. Quotation methods
d. Exotics
e. The Vanna-Volga model
Textbooks
Hull, Opzioni, Futures e altri derivati, Pearson Ed.
Additional reading:
Brigo e Mercurio, Interest Rate Models-theory and Practice: With Smile, Inflation and Credit, Springer Ed.
Brigo, Morini, Pallavicini, Counterparty Credit Risk, Collateral and Funding, Wiley Ed.
Castagna, FX Options and Smile Risk, Wiley Ed.
Examination Methods
Written exam (70%) + Project Work (30%).
The Project Work, to be decided with the Teacher, is a small paper, with length less than 10 pages, dealing with one of the following jobs:
1) application of a model to market data
2) a simulation or numerical approximation of proposed models
3) the valuation of a contract involving derivatives
4) a valuable discussion of some part of the theory
5) the discussion of a recent scientific article
The Project Work needs to be completed to gain access to the written exam.
