Teaching code

4S00535

Teacher

Immacolata Oliva

Coordinator

Immacolata Oliva

Credits

6

Language

Italian

Scientific Disciplinary Sector (SSD)

SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES

Period

Primo Semestre Magistrali dal Oct 2, 2017 al Dec 22, 2017.

Lessons timetable Moodle Seminars 0

Learning outcomes

The course aims at analyzing the main numerical methods for derivative pricing and risk managment, in particular:

- tree methods;

- finite differences methods (implicit, explicit, Crank-Nicholson)

- Monte Carlo methods.

At the end of the course, students are able to efficiently implement the previous methods, by using Matlab.


Although no formal prerequisites is needed, the knowledge of the topics related to Stochastic Models for Finance and Mathematical Finance is strongly recommended.

Program

the main goal of the course is the introduction of the main numerical methods used for numerical computation of financial quantities, derivative pricing and risk evaluation in finance. Such methods will be developed with the use of the software Matlab.

In particular, the following topics will be treated:

- Tree methods for the pricing of European contingent claims and empirical check of the convergence of the results to the Black and Scholes formula in the case of put and call options. Computation of the delta. Application of the methods in the case of American contingent claims.

- Finite differences methods (implicit, explicit, Crank-Nicholson) for the pricing of European and American contingent claims. Stability and convergence.

- Monte Carlo methods: Euler scheme for the simulation of trajectories of stochastic processes. Use of Monte Carlo methods for derivative pricing.

TEXTBOOKS:

P. Glasserman, "Monte Carlo Methods for Financial Engineering", Springer (2004)

L. Clewlow and C. Strickland, "Implementing Derivatives Models", Wiley (1998)

F. D. Rouah and S. L. Heston "The Heston Model and its Extensions in Matlab and C#", Wiley (2013)

Examination Methods

The exam consists in a practical work with Matlab, organized in exercises and/or essay questions.

The oral test is optional, and it is devoted to the assessment of student's learning during the course, the understanding of items and the ability to connect knowledges.