Tutorial in financial modeling

Overview

The fast growth of asset management industry during the past few decades highlighted the analysis of portfolio allocation performance as an important aspect of modern finance. Research in this area is axed on Sharpe-like ratios proposed in the 1960’s. The major drawbacks of these techniques are on the one hand the identification of benchmark portfolios and on the other that they suffer from significant estimation errors. The latter prevents any performance comparison to be significant.

volesti provides the computation (few milliseconds for stock markets with thousands of assets) of the score of a portfolio defined as the percentage of all possible portfolios that it has outperformed, in terms of return. An important advantage of this score is that it makes the score robust against shocks hitting equally all asset returns, such as risk-free shocks in the classical APT model, and volatility jumps. This score combined with a similar score on volatility can be used to detect financial crises in big stock markets.

The usability of these components in volesti is limited since most of them lack proper documentation and are provided as computations related to geometrical problems and not to FinTech. Thus, these algorithmic and computational tools are not easy accesible by FinTech community. The aim of this project is to write a tutorial and a documentation to highlight these tools and make them easily accessible to researchers or asset managers.

Details of your coding project

The project splits in the following tasks:

• Documentation and tutorial for the portfolio score computations and comparison with other alternatives.
• Documentation and tutorial for sampling uniformly distributed portfolios.
• Documentation and tutorial for copula construction to describe return-volatility relation in a given time period.
• Documentation and tutorial for crises detection using copulae.

Mentors

Students, please contact both mentors below after completing at least one of the tests below.

• Vissarion Fisikopoulos <vissarion.fisikopoulos at gmail.com> is an expert in mathematical software, computational geometry and optimization, and has previous GSOC mentoring experience with Boost C++ libraries (2016-2019) and the R-project (2017-2019).

• Apostolos Chalkis <tolis.chal at gmail.com> is a PhD student in Computer Science. His research focuses on mathematical computing, optimization and computational finance. He has previous experience in GSoC 2018 and 2019 as a student under Org. R-project, implementing state-of-the-art algorithms for sampling from high dimensional multivariate distributions. He is one of the authors of volesti.

• Elias Tsigaridas <elias.tsigaridas at inria.fr> is an expert in computational nonlinear algebra and geometry with experience in mathematical software. He has contributed to the implementation, in C and C++, of several solving algorithms for various open source computer algebra libraries and has previous GSOC mentoring experience with the R-project (2019).