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 |
|---|
| Modules | Credits | TAF | SSD |
|---|
| 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.
Numerical methods for mathematical finance (seminar course) (2014/2015)
Teaching code
4S001114
Teacher
Coordinator
Credits
6
Language
Italian
Scientific Disciplinary Sector (SSD)
MAT/08 - NUMERICAL ANALYSIS
Period
II sem. dal Mar 2, 2015 al Jun 12, 2015.
Learning outcomes
In this course we will study basic numerical methods for option pricing.
Program
Binary Trees
- riskless portfolio
- risk neutral probability
- calibrating the tree
Continuous Time
- Geometric Brownian Motion
- the Black-Scholes PDE
- Feynman-Kac and risk-neutrality
Estimating the Volatility from historical data
Acceleration of the backfolding of the tree using the FFT
Other fast(er) methods for trees
Path Dependent Options using a Tree
- Lookback Puts and Calls
- the Cheuk-Vorst algorithm
- American Lookback options
Numerical Methods for Advection-Diffusion Equations
- Euler Explicit
- Euler Implicit
- Crank-Nicholson
- application to the Black-Scholes PDE
Asian Options
- an associated PDE
- eliminating the advection term
American Options
- linear complementary problems
- numerical solution
The Carr-Madan Fourier algorithm (for a call)
Jump Diffusion Models
- compound Poisson processes and their simulation
- the Merton Model
- the Merton formula
- the Carr-Madan algorithm for the Merton Model
- American options under the Merton Model
The fast Gauss Transform and its application to Option Pricing
Calibration using Hisorical Data
- the Schwartz Mean Reverting Model for Comodities
- its calibration using Forward Prices
Monte Carlo Methods
- accelerations
- application to Basket Options
Discretization of SDEs
- Euler discretization
- Milstein discretization
Examination Methods
The final mark will be bsed on homework assignments as well as a project completed by the student.
