Ing Ind - Inf (Mag.)(ord. 270) - MI (487) MATHEMATICAL ENGINEERING - INGEGNERIA MATEMATICA

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ZZZZ

097658 - COMPUTATIONAL FINANCE

097667 - COMPUTATIONAL FINANCE

Obiettivi dell'insegnamento

The aim of the course is to make students familiar with the advanced quantitative methods adopted in describing the dynamics of financial markets, in valuating and hedging financial derivatives, and in optimal investments problems. An implementation of all models and methods in Matlab is an essential part of the program. The goal is to provide students with all the instruments necessary to be able to solve a financial problem, like pricing derivatives, choosing the best model and coding to obtain a numerical solution. A part of the course is also devoted to Fintech applications.

This course is connected to the joint-course 097667 - COMPUTATIONAL FINANCE (8 cfu). This sheet defines objectives, programs and learning outcomes expected for both courses.

Risultati di apprendimento attesi

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

- 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.

- Ability in applying knowledge and understanding

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

- 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).

- 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; fondamental properties of Lévy processes and reason why they overcome the Black&Scholes limits; Lévy-Kintchine formula; simulating Lévy processes.

Asset Allocation: Hamilton-Jacobi-Bellman equation in optimal allocation problems; managing assets' portfolio. [only for the 10 cfu version]

Numerical Methods for Finance

Monte Carlo Simulations: random numbers generator; sampling from uniform and normal distribution; Quasi Monte Carlo methods; 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 and Finite Elements discretizations: evaluating barrier and European options via Finite Differences and Finite Elements; pricing American derivatives: the PSOR algorithm.

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

Energy Finance[only for the 10 cfu version]

Energy commodities; Valuation of a Swing option on Gas

Prerequisiti

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: a) projects on energy finance and asset allocation topics; b) coding exam; c) oral exam.

The objective of projects is to let students work in groups, applying the approaches and principles taught in class. Projects will be assigned through the semester. Project artifacts are expected to be released at fixed deadlines that will be defined by the time the project will be assigned. The evaluation of projects will be based on the produced artifacts (documentation, code, …).

The maximum mark for projects is 5/30. The maximum mark for the coding exam is 25/30. In order to be admitted to the oral exam the sum of the two marks must be at least 18/30. The oral exam is mandatory, and it could result in a maximum increase of the final mark of 3/30 points.

For the course 097667 - COMPUTATIONAL FINANCE (8 cfu) no projects are required. The maximum mark for the coding exam is 30/30. The oral exam is mandatory, and it could result in a maximum increase of the final mark of 3/30 points.

The exam has the goal of checking whether the student has acquired the following skills: - knowledge of advanced concepts of stochastic calculus, which are essential in quantitative finance; - knowledge of how to choose modeling assumptions to solve a financial problem properly; - ability to write a code/algorithm to solve a financial problem, exploiting the developed theoretical knowledgements; - ability to find proper modeling assumption to describe a financial asset (like interest rate, volatility, commodities, etc.); - ability to express mathematical and financial concepts in a clear and rigorous way.

Bibliografia

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

Forme didattiche

Tipo Forma Didattica

Ore di attività svolte in aula

(hh:mm)

Ore di studio autonome

(hh:mm)

Lezione

60:00

90:00

Esercitazione

0:00

0:00

Laboratorio Informatico

40:00

60:00

Laboratorio Sperimentale

0:00

0:00

Laboratorio Di Progetto

0:00

0:00

Totale

100:00

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