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. 2016/2017
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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.
Mathematical finance (2015/2016)
Teaching code
4S001142
Teacher
Coordinator
Credits
9
Language
Italian
Scientific Disciplinary Sector (SSD)
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES
Period
Secondo Semestre Magistrali dal Feb 22, 2016 al Jun 1, 2016.
Learning outcomes
The course is an introduction to the main theoretical models of quantitative finance with particular emphasis on the study of non arbitrage principle by introducing discrete and continuous time models. The course includes exercises on the arguments developed in MATLAB.
Prerequisites
Although no formal prerequisites for successful learning, it is recommended that you have already passed the test of Stochastic Models for finance in the first half.
Program
First part: The principle of non arbitrage and the derivatives pricing in discrete time
One period market. Arrow and Debreu securities. Portfolios of securities. Replicable securities. Complete and incomplete markets. Market equilibrium and arbitrage of the first and second kind. Non arbitrage principle and law of one price. Fundamental theorem of Finance (TFF). Risk neutral probabilities. Non arbitrage price of a security. Derivatives: definition and properties. Self financing portfolios. Multiperiod market: binomial tree model of Cox Ross and Rubinstein (CRR). Discret martingale processes. Risk neutral evaluation and replication of put and call options.
Second part: the principle of arbitrage and the derivatives pricing in continuous time
A market model in continuous time: the geometric Brownian motion. Stochastic calculus tools: stochastic differential equations. Continuous martingale processes. Normal and lognormal processes. Self financing portfolios. Replicable securities. Absence of arbitrage and completeness. Non arbitrage price of a title. Equivalent martingale measure. Girsanov's theorem. Feynman-Kac theorem. Black and Scholes Formula and its derivation. Delta hedging.
Textbooks
Teaching material is available online by accessing the e-learning page. Please refer also to the following books for the first part:
S. Pliska: Introduction to Mathematical Finance. Blackwell, 1997.
for thesecond part:
F. Menoncin: Mercati finanziari e gestione del rischio, Isedi, 2006.
Lessons
The lessons, for a total of 54 hours, are held in a classroom equipped with computers and dedicated software.
Examination Methods
The exam consists of a written test and an oral test. The written test consists in the resolution of four years. During the written test is allowed to use calculator only and you may not use lecture notes or other teaching material. Are allowed to take the oral test only students who have reported a mark greater than or equal to 16/30 in the written test.
