Teaching code

4S00535

Teacher

Andrea Mazzon

Coordinator

Andrea Mazzon

Credits

6

Language

Italian

Scientific Disciplinary Sector (SSD)

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

Period

Primo semestre (lauree magistrali) dal Oct 2, 2023 al Dec 22, 2023.

Courses Single

Authorized

Lessons timetable Moodle Seminars 0

Learning objectives

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, tudents 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.

Prerequisites and basic notions

Good knowledge of the Java programming language and of the most important concepts of Financial Mathematics in discrete and continuous time.

Program

1. Use of tree methods with application to the valuation of financial derivatives: we will see how to price European and path dependent derivatives through the use of binomial and trinomial trees. In particular, we will initially focus on European and barrier options.
2. Monte Carlo simulation of stochastic processes with application to the valuation of financial derivatives: in particular, we will discuss the Euler-Maruyama and Milstein methods for the discretization of SDEs, and their implementation for the approximation of the expected value of a payoff depending on the solution of the SDEs . We will look at the advantages and disadvantages of using these techniques when evaluating European derivatives and barrier options.
3.numerical solution of PDE with application to the evaluation of financial derivatives: we will see that the Feynman-Kac formula allows us to evaluate a financial derivative also through the numerical solution of a PDE, whose coefficients are associated with those of the SDE resolved by the underlying. We will therefore see the classic finite difference numerical methods: explicit and implicit Newton and Crank-Nicolson. We will also be able to compare the results obtained in this way with those given by the methods described above.
4. Valuation of American and Bermudan options: finally, we will focus on derivatives whose owner has the right to exercise before maturity: we will see the problems inherent in the valuation of these options and the most commonly used numerical techniques. We will also see how the three methods seen above (trees, Monte Carlo with discretization of SDEs, numerical solution of PDEs) behave in this context.

Didactic methods

Lectures in presence with recordings made available to students

Learning assessment procedures

Written exam and delivery of a Java project on one or more topics of the course

Evaluation criteria

For what concerns the written exam, the student is required to demonstrate a critical and in-depth knowledge of the topics covered in the course, both in terms of the more theoretical and code-related aspects. The answers must be precise and strictly relevant to the main topics of the questions.
The Java project must be able to run without errors and provide the expected results. It must also follow the best practices that we will discuss in the course, and in particular be well documented.

Criteria for the composition of the final grade

The written exam constitutes 80% of the final score, the Java project the remaining 20%.

Exam language

Italiano