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 Mathematics - 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
| Modules | Credits | TAF | SSD |
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| Modules | Credits | TAF | SSD |
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| Modules | Credits | TAF | SSD |
|---|
three course to be chosen among the followingA 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 (2014/2015)
Teaching code
4S001109
Credits
6
Language
English
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 internationalized 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 the 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.
Program
Discrete time models
• Contingent claims, value process, hedging strategies, completeness, arbitrage
• Fundamental theorems of Asset Pricing (in discrete time)
The Binomial model for Assset Pricing
• One period / multiperiod Binomial model
• A Random Walk (RW) interlude (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 Values
• Solution to the Black-Scholes-Merton Equation
• Sensitivity 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, American 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
There will be a written final exam.
