Ing Ind - Inf (Mag.)(ord. 270) - MI (487) MATHEMATICAL ENGINEERING - INGEGNERIA MATEMATICA
097667 - COMPUTATIONAL FINANCE
097658 - COMPUTATIONAL FINANCE
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.
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
Bitcoin and Blockchain Technologies[only for the 10 cfu version]
Hash functions and elliptic curve cryptography; Blockchain and Merkle tree; Distributed consensus and mining; Transactions; Bitcoin Core; Wallets
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 the fintech 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.
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
Tipo Forma Didattica
Ore di attività svolte in aula
Ore di studio autonome
Laboratorio Di Progetto
Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua
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