Course Details for A.Y. 2017/2018
Name:
Processi Stocastici Per La Finanza / Stochastic processes in Finance
Basic information
Credits:
: Master Degree in Mathematics 6 CFU (c)
Degree(s):
Master Degree in Mathematics 2nd anno curriculum Generale Elective
Language:
Italian
Course Objectives
Students shuould acquire a good knowledge of advanced probabilistic tools employed in the modeling of
financial markets.
In particular they should become able to
- learn and understand the first mathematical models involving stochastic calculus techniques;
- solve derivatives evaluation problems of medium difficulty;
- extend the studied notions to more complex models;
- read an advanced text in financial modeling;
- implement computations for the studied models.
Course Content
- Complements of stochastic calculus. The martingale representation theorem,
Girsanov theorem, existence and uniqueness of the solutions of stochastic differential
equations, quadratic variation.
- Balck and Scholes world. European options evaluation, Barrier options, American options, (perpetual puts and critical price).
Option evaluation for a general diffusion model: the infinitesimal generator of a diffusion, computation of expectations and
partial differential equations
The multidimensional model: viability and completeness.
Asian options and exchange options.
- Bonds and interst rate models. Zero coupon bonds. Merton model, Vasicek model,
Cox Ingersoll Ross model
- Weak solutions of stochastic differential equations. weak solutions via Girsanov. Yamada and
Watanabe's results. The unidimensional case.
- Stochastic volatility models. Stein and Stein, Hull and White, Heston models
Learning Outcomes (Dublin Descriptors)
On successful completion of this course, the student should
- Students shuould acquire a good knowledge of advanced probabilistic tools employed in the modeling of
financial markets.
- students should become able to
- learn and understand the first mathematical models involving stochastic calculus techniques;
- solve derivatives evaluation problems of medium difficulty;
- students should become able to
- solve derivatives evaluation problems of medium difficulty;
- extend the studied notions to more complex models;
- Students should become able to expose the main points of financial modeling to an audience of experts and
non experts.
- students should become able to
- read an advanced text in financial modeling;
- implement computations for the studied models.
Prerequisites and Learning Activities
An advanced course in probability and the first part of the integrated course
Assessment Methods and Criteria
oral exam
Textbooks
- I. Karatzas, S. Shreve, Brownian motion and stochastic calculus , Springer.
- A. Pascucci, Calcolo Stocastico per la Finanza , Springer.
- D. Lamberton, D. Lapeyre, Introduction to stochastic calculus applied to Finance , Chapman and Ha.
- J. Zhu, Modular pricing of options (Lecture notes in Economics and Mathematical Systems) , Springer. (vol. 493)
- P.E. Kloeden, E. Platen, Numerical Solution of Stochastic Differential Equations , Springer.
- P. Billingsley, Probability and measure , Wiley . 1984.
Course page updates
This course page is available (with possible updates) also for the following academic years:
To read the current information on this course, if it is still available, go to the university course catalogue .
Course information last updated on: 18 marzo 2015, 17:45