# MATHEMATICAL MODELS IN FINANCE MOD. 1 cod. 1006141

1° year of course - First semester
Professor
- Chiara GUARDASONI
Analisi numerica (MAT/08)
Field
A scelta dello studente
Type of training activity
Student's choice
48 hours
of face-to-face activities
6 credits
hub: PARMA
course unit
in ITALIAN

Integrated course unit module: MATHEMATICAL MODELS IN FINANCE

## Learning objectives

- Knowledge of language and technical procedures typical of Mathematical Finance. Ability to understand numerical methods for the resolution of differential problems arising from derivatives evalutation in Finance.

- Ability to apply knowledge and understanding in the critical analysis of the numerical results obtained giving a financial interpretation.

- Autonomy of judgment in evaluating the approximation algorithms and the obtained results also through discussion with one's peers.

- Ability to communicate clearly the acquired concepts and to discuss the obtained results.

- Ability to learn limits and advantages of models and methods of resolution and to apply them in different working and scientific contexts.

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## Course unit content

Description of some types of financial options and of differential models that model their evaluation. Description and analysis of numerical methods for the resolution of these differential models.

## Full programme

- Black & Scholes (BS) model for the evaluation of European financial options.
- Numerical methods for the resolution of the BS model: implicit and explicit finite difference methods, finite element method, binomial method.
- Financial options with barriers and boundary element method.
- Multiasset options.
- Asian options.

## Bibliography

Most of the program is based on:

- P.Wilmott, J. Dewynne and S. Howison, 'Option Pricing', Oxford Financial Press, 1993

- R. Seydel, 'Tools for Computational Finance', Springer, 2009

## Teaching methods

During the lectures the contents of the course will be analyzed, highlighting the difficulties related to the introduced numerical techniques. Moreover, the course will consist of a part of supervised cooperative learning consisting in the application of the numerical techniques through laboratory programming in Matlab. This activity will allow students to acquire the ability to deal with "numerical" difficulties, it will allow to evaluate the reliability and consistency of the obtained results and to analyse them from a financial point of view.
A week of teaching will be held by Prof. Luis Ortiz-Gracia, professor of Quantitative Finance at the University of Barcelona, who will also be able to transfer his acquired skills in the experience as a practitioner. The course will take place online or in presence according to University guidelines.

## Assessment methods and criteria

The exam consists of
an assessment of the knowledge through a discussion of topics of the course or of a deepening job carried out autonomously by the candidate on a specific task. The threshold of sufficiency consists in the knowledge of the characteristics that allow to evaluate efficiency and stability of a numerical method and the knowledge of some foundations of quantitative finance illustrated during the course.

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