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
Queste informazioni sono destinate esclusivamente agli studenti e alle studentesse già iscritti a questo corso. Se sei un nuovo studente interessato all'immatricolazione, trovi le informazioni sul percorso di studi alla pagina del corso:
Laurea magistrale in Mathematics - Immatricolazione dal 2025/2026.The 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
| Modules | Credits | TAF | SSD |
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| Modules | Credits | TAF | SSD |
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| Modules | Credits | TAF | SSD |
|---|
A course to be chosen among the followingLegend | 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.
Mathematical finance (2013/2014)
Teaching code
4S001109
Credits
6
Language
English
Location
VERONA
Scientific Disciplinary Sector (SSD)
MAT/06 - PROBABILITY AND STATISTICS
The teaching is organized as follows:
Teoria 2
Esercitazioni
Teoria 1
Learning outcomes
The Mathematical Finance course for the internationallized Master's Degree (delivered completely in English) aims to introduce the main concepts of stochastic discrete and continuous time part of the modern theory of financial markets. In particular, the fundamental purpose of the course is to provide the mathematical tools characterizing the setting of Itȏ stochastic calculus for the determination, the study and the analysis of models for options and / or interest rates determined by stochastic differential equations driven by Brownian motion. Basic ingredients are the foundation of the theory of continuous-time martingale, Girsanov theorems and Faynman-Kac theorem and their applications to the theory of option pricing with specific examples in equities, also considering path-dependent options, and within the framework of interest rates models.
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Please refer to: http://lucadipersio.wordpress.com/ for details about the course: course material, seminars, special events, etc. [ in particular take a look to the Teaching area and the "principal page" of annuncements ]
Program
Discrete time models
Contingent claims, value process, hedging strategies, completness, arbitrage
Fundamental theorems of Asset Pricing (in discrete time)
The Binomial model for Assset Pricing
One period / multiperiod Binomial model
A Random Walk (RW) interludio (scaled RW, symmetric RW, martingale property and quadratic variation of the symmetric RW, limiting distribution)
Derivation of the Black-Scholes formula (continuous-time limit)
Brownian Motion (BM)
review of the main properties of the BM: filtration generated by BM, martingale property, quadratic variation, volatility, reflection properties, etc.
Stochastic Calculus
Itȏ's integral
Itȏ-Döblin formula
Black-Scholes-Merton Equation
Evolution of Portfolio/Option Value
Solution to the Black-Scholes-Merton Equation
Sensitiveness analysis
Risk-Neutral Pricing
Risk-Neutral Measure and Girsanov's Theorem
Pricing under the Risk-Neutral Measure
Fundamental Theorems of Asset Pricing
Existence/uniqueness of the Risk-Neutral Measure
Dividend/continuously-Paying
Forwards and Futures
Stochastic Differential Equations
The Markov Property
Interest Rate Models
Multidimensional Feynman-Kac Theorems
Lookback, asian, amaerican Option
Term structure models
Affine-Yield Models
Two-Factor Vasicek Model
Two-Factor CIR Model
Heath-Jarrow-Morton (HJM) Model
HJM Under Risk-Neutral Measure
Examination Methods
Written exam
