Risorse bibliografiche
Risorsa bibliografica obbligatoria
Risorsa bibliografica facoltativa
Scheda Riassuntiva
Anno Accademico 2024/2025
Scuola Scuola di Ingegneria Industriale e dell'Informazione
Insegnamento 062161 - COMPUTATIONAL FINANCE
Cfu 10.00 Tipo insegnamento Monodisciplinare
Docenti: Titolare (Co-titolari) Marazzina Daniele

Corso di Studi Codice Piano di Studio preventivamente approvato Da (compreso) A (escluso) Insegnamento

Obiettivi dell'insegnamento

The course aims to familiarize students with advanced quantitative methods used to describe financial market dynamics, value and hedge financial derivatives, and solve optimal investment problems. An integral component of the program is the implementation of these models and methods in MATLAB. The objective is to equip students with the tools necessary to solve financial problems, such as pricing derivatives, selecting optimal models, and coding to obtain numerical solutions. Additionally, a portion of the course is dedicated to exploring applications in asset allocation and in the energy market.

This course is closely linked to the joint-course "Computational Finance" (8 CFU). The provided outline defines the objectives, curriculum, and expected learning outcomes for both courses.

Risultati di apprendimento attesi

Lectures and coding sessions will allow students to acquire the following competences:

- DD1 Knowledge and understanding

know some advanced concept of stochastic calculus, which are essential in quantitative finance;
know how to choose modeling assumptions to solve a financial problem properly.

- DD2 Ability in applying knowledge and understanding

know how to write a code/algorithm to solve a financial problem, exploiting the developed theoretical knowledgements.

- DD3 Making judgements

find proper modeling assumption to describe a financial asset (like interest rate, volatility, commodities, etc.);
be able to judge the possible financial risks raising from using wrong modeling assumption (like misprice of financial products).

- DD4 Communication skills

to be able to express mathematical and financial concepts in a clear and rigorous way.

Argomenti trattati

Advanced Models for Financial Markets and Asset Allocation

Lévy processes: stochastic calculus for jump processes; fundamental properties of Lévy processes and reason why they overcome the Black&Scholes limits; Lévy-Kintchine formula; simulating Lévy processes; approximate small jumps with a Wiener process; construction of Lévy processes by subordination; Lévy-Ito formula

Stochastic Volatility models: Heston, Hull-White, Stein & Stein models.

Stochastic volatility models with jumps: Bates, BNS, time change Lévy

Numerical Methods for Finance

Monte Carlo Simulations: sampling from uniform and other distributions; simulating continuous processes; simulating jump diffusion processes; variance reduction techniques; pricing European and exotic options; pricing American derivatives: the Longstaff & Schwarz algorithm.

PDE: Finite Differences discretizations: evaluating barrier and European options via Finite Differences; pricing American derivatives: the PSOR algorithm. 

FFT: Carr-Madan method for European derivatives. The Convolution method

Energy Finance 

Energy commodities; Jump processes for commodities; Valuation of a Swing option on Gas

Asset Allocation

Black&Litterman approach; asset allocation and efficient portfolio frontier

For the 8 cfu version: you can choose between the Energy Finance and Asset Allocation

For the 10 cfu version: all parts are mandatory

Obiettivi di sviluppo sostenibile - SDGs
Questo insegnamento contribuisce al raggiungimento dei seguenti Obiettivi di Sviluppo Sostenibile dell'Agenda ONU 2030:


Students are required to know the following topics.

- stochastic calculus: Wiener process, martingale, filtration.
- finance: option pricing in the Black&Scholes framework.
- coding: Matlab.

Modalità di valutazione

The exam consists of three components:

a) Projects: Students will work in groups on projects related to energy finance and asset allocation topics. Projects will be assigned throughout the semester with fixed deadlines. Evaluation will be based on project artifacts such as documentation and code. The maximum mark for projects is 8/30, with 4 points allocated to each project.

b) Coding Exam: A coding exam will assess students' ability to write code or algorithms to solve financial problems using advanced concepts of stochastic calculus. The maximum mark for the coding exam is 20/30.

c) Theoretical Exam: Theoretical knowledge of advanced concepts in stochastic calculus and quantitative finance will be tested. The theoretical exam is mandatory and can result in a maximum increase of 5/30 points.

For the course "Computational Finance" (8 CFU), only one of the two projects is required, evaluated 8/30. The maximum mark for the coding exam is 20/30. The theoretical exam is mandatory and can result in a maximum increase of the final mark of 5/30 points.

Overall, the exam assesses students' skills in understanding advanced financial concepts, applying theoretical knowledge to solve problems, writing code to implement financial models, and expressing mathematical and financial concepts clearly and rigorously.

Risorsa bibliografica facoltativaR. Cont, P. Tankov, Financial Modelling with Jump Processes, Editore: CRC/CHAPMAN-HALL, Anno edizione: 2004
Risorsa bibliografica facoltativaR. Seydel, Tool for Computational Finance, Editore: Springer-Verlag, Anno edizione: 2012

Software utilizzato
Nessun software richiesto

Forme didattiche
Forma Didattica Ore Didattica Assistita
% Didattica Assistita
40.0 %
60.0 %
0.0 %
0.0 %
0.0 %
Totale ore didattica assistita (hh:mm) 100:00
Totale ore di studio autonomo (hh:mm) 150:00

Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua Inglese
Disponibilità di materiale didattico/slides in lingua inglese
Disponibilità di libri di testo/bibliografia in lingua inglese
Possibilità di sostenere l'esame in lingua inglese
Disponibilità di supporto didattico in lingua inglese
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