Fakulta matematiky, fyziky
a informatiky
Univerzita Komenského v Bratislave

STRIKE - Novel Methods in Computational Finance (FP7 Marie Curie Action, Project Multi-ITN)

In recent years the computational complexity of mathematical models employed in financial mathematics has witnessed a tremendous growth. Advanced numerical techniques are imperative for the most present-day applications in financial industry. The motivation for this training network is the need for a network of highly educated European scientists in the field of financial mathematics and computational science, so as to exchange and discuss current insights and ideas, and to lay groundwork for future collaborations.

25. 11. 2015 13.09 hod.
Od: Daniel Ševčovič

Zodpovedný riešiteľ: prof. RNDr. Daniel Ševčovič, CSc.
Spoluriešeitelia: Mgr. Soňa Kilianová, PhD., RNDr. Mária Trnovská, PhD., Mgr. Pedro Pólvora, Mgr. Silvie Kafková, PhD.
Financovanie projektu: European Union in the FP7-PEOPLE-2012-ITN Program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE - Novel Methods in Computational Finance)
Contract: PITN-GA-2012-304617 STRIKE
Obdobie riešenia projektu: 2013-2016
Stránka projektu na FMFI UK: http://www.iam.fmph.uniba.sk/institute/sevcovic/strike/ 
Stránka projektu pre EÚ: http://www-amna.math.uni-wuppertal.de/itn-strike/

Besides a series of internationally recognized researchers from academics, leading quantitative analysts from the financial industry also participate in this network. The challenge lies in the necessity of combining transferable techniques and skills such as mathematical analysis, sophisticated numerical methods and stochastic simulation methods with deep qualitative and quantitative understanding of mathematical models arising from financial markets. The main training objective is to prepare, at the highest possible level, young researchers with a broad scope of scientific knowledge and to teach transferable skills, like social awareness which is very important in view of the recent financial crises. The current topic in this network is that the financial crisis in the European countries is a contagion and herding effect and is clearly outside of the domain of validity of Black-Scholes and Merton’s theory, since the market is not Gaussian and it is not frictionless and complete. In this research training network our aim is to deeper understand complex (mostly nonlinear) financial models and to develop effective and robust numerical schemes for solving linear and nonlinear problems arising from the mathematical theory of pricing financial derivatives and related financial products. This aim will be accomplished by means of financial modelling, mathematical analysis and numerical simulations, optimal control techniques and validation of models.

Bratislava team is the project leader in the Workpackage WP1: Modelling and Analysis. The goal is to investigate qualitative and quantitative properties of solutions to nonlinear generalizations of the Black-Scholes (BS) equation. Nonlinear models can capture several important phenomena like transaction costs, investor's risk from unprotected portfolio, investor's expected utility maximization, illiquid markets, large traders feedback influence, etc.

Such generalizations can be mathematically stated in the form of a nonlinear BS equation in which the volatility is adjusted to be a function of the Gamma of the option. Our approach is based on the analysis of the nonlinear BS equation for the Gamma of the option by means of combination of fully implicit and explicit finite difference methods (FDMs).