Course Details for A.Y. 2017/2018

The information on this page refer to the academic year 2017/2018. Therefore, several links are not available and data may be incomplete. To read the current information on the course, if it is still available, go to the university course catalogue . To read information relating other academic years, use the list at the bottom of this page.

A. Year:

2017/2018

Name:

Processi Stocastici Per La Finanza / Stochastic processes in Finance

Type:

Course

Basic information

Code:

F0985

Sector:

MAT/06

Credits:

: Master Degree in Mathematics 6 CFU (c)

Term:

1^st semester

Degree(s):

Master Degree in Mathematics 2^nd anno curriculum Generale Elective

Language:

Italian

Teacher(s):

Fabio Antonelli

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