Quantitative Finance and Insurance

The course aims at presenting some numerical techniques used in financial applications. The students will be working with Python in the first part of the course and will be introduced to the MATLAB software in the second part of the course.

Ability to handle numerical techniques suitable for financial problems in Python and Matlab.

 The first 16 hours of the course will be taught by prof. Jan Palczewsky and the remaining 16 hours by prof. Luca Regis.

Please download the last version of MATLAB using Unito campus licence and be ready to work on the software during classes.

 

Weekly assignments will have to be delivered during the course. They will constitute a coursework, to be delivered to pass the exam. 

The final exam consists of a group project.

Projects must be chosen among a list that we will provide by the end of the course.

Groups should be composed of max 3-4 people.

The discussion of the project will consist in a short presentation of

the project.

The group is also expected to deliver a short report in

pdf format, containing:

- a description of the financial and mathematical problem;

- a description of the solution of the problem;

- the explanation of the numerical algorithms adopted;

- Code scripts and user-defined functions;

- discussion of the results.

As a general rule, try to write the code in the most efficient possible way, trying

to avoid for loops when possible by vectorizing the calculations.

I will supervise the projects and assist the groups in making the code.

 

    - Financial applications with Python: 

* Option pricing using binomial trees
* Monte Carlo methods for option pricing in Black-Scholes model
* Variance reduction techniques
* Numerical solution of stochastic differential equations and pricing in non-Black-Scholes markets
* Computation of Greeks and portfolio immunisation

- Programming and Financial Applications with MATLAB:

  * MATLAB Basics

  * Data handling with MATLAB

  * Generation of paths of jump/diffusive and jump stochastic processes

  * Monte Carlo simulation of portfolio dynamics and computation of risk measures

 

 

We will provide lecture notes and slides as course material.

Further resources that can prove to be useful are the following:

MAIN ONLINE FREE RESOURCES:

https://it.mathworks.com/help/matlab/

 

ADDITIONAL BOOKS AND ARTICLES:

P. Brandimarte, 2006, Numerical methods in finance and economics: a MATLAB-based introduction, Wiley.